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![Page 1: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/1.jpg)
Calculations with significant figures
So now you know how to determine the number of significant figures in a number and how to round numbers off, what good does that do?
![Page 2: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/2.jpg)
Calculations with significant figures
Well, let’s consider the rectangle below. If we want to determine the area of the rectangle, the easiest way would be to measure the length and the height, and then multiply these two numbers together. (For rectangles, Area = Length x Height.)
![Page 3: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/3.jpg)
Calculations with significant figures
First let’s measure the length: a correct reading might be something like 36.3 cm (…or 36.2 cm or 36.4 cm)
0 10cm
20 30 40 50
![Page 4: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/4.jpg)
Calculations with significant figures
Now let’s measure the height: for height, a correct reading might be some- thing like 6.7 cm (…or 6.6 cm or 6.8 cm).
010
cm20
![Page 5: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/5.jpg)
Calculations with significant figures
So let’s multiply these two numbers:
![Page 6: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/6.jpg)
Calculations with significant figures
So let’s multiply these two numbers:
36.3 x 6.7 = 243.21 (and cm x cm = cm2).
So we have 243.21 cm2. But if we state the area to be 243.21cm2, we are stating a pretty high level of precision.
![Page 7: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/7.jpg)
Calculations with significant figures
But if we say the area is 243.21cm2, we are saying we know the area to a very high level of precision.
![Page 8: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/8.jpg)
Calculations with significant figures
But if we say the area is 243.21cm2, we are saying we know the area to a very high level of precision. We are saying that we are certain of the “243.2..” and that we are guessing the “1.”
![Page 9: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/9.jpg)
Calculations with significant figures
But if 36.2 cm long and 6.6 cm high were also correct measurements, then 36.2 cm x 6.6 cm = 238.92 cm2 would have to be a correct area for the same rectangle.
![Page 10: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/10.jpg)
Calculations with significant figures
But if 36.2 cm long and 6.6 cm high were also correct measurements, then 36.2 cm x 6.6 cm = 238.92 cm2 would have to be a correct area for the same rectangle. That implies we are certain of the “238.9…” and only guessing the “2.”
![Page 11: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/11.jpg)
Calculations with significant figures
And if 36.4 cm long and 6.8 cm high were also correct measurements, then 36.4 cm x 6.8 cm = 247.52 cm2 would also have to be a correct area for the same rectangle.
![Page 12: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/12.jpg)
Calculations with significant figures
And if 36.4 cm long and 6.8 cm high were also correct measurements, then 36.4 cm x 6.8 cm = 247.52 cm2 would also have to be a correct area for the same rectangle. That implies we are certain of the “247.5…” and only guessing the “2.”
![Page 13: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/13.jpg)
Calculations with significant figures
243.21 cm2, 238.92 cm2 and 247.52 cm2
![Page 14: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/14.jpg)
Calculations with significant figures
243.21 cm2, 238.92 cm2 and 247.52 cm2 These three values cannot all be correct.
![Page 15: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/15.jpg)
Calculations with significant figures
243.21 cm2, 238.92 cm2 and 247.52 cm2 These three values cannot all be correct. The only digit that seems to be definite is the first “2” (in the hundreds place). After that the values are not at all consistent with one another.
![Page 16: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/16.jpg)
Calculations with significant figures
This would mean that our guess should be the second digit (in the tens place), and that the values should all be rounded there – to two significant figures.
![Page 17: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/17.jpg)
Calculations with significant figures
243.21 cm2 rounds to 240 cm2 238.92 cm2 rounds to 240 cm2 and 247.52 cm2 rounds to 250 cm2.
![Page 18: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/18.jpg)
Calculations with significant figures
240 cm2, 240 cm2 and 250 cm2.
![Page 19: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/19.jpg)
Calculations with significant figures
240 cm2, 240 cm2 and 250 cm2. These are all consistent with one another.
![Page 20: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/20.jpg)
Calculations with significant figures
240 cm2, 240 cm2 and 250 cm2. These are all consistent with one another. They all have two significant figures, and they show disagreement only in the guessed digit.
![Page 21: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/21.jpg)
Calculations with significant figures
Is there a way we could have known from the beginning that our answer needed to be rounded to only two significant figures?
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Calculations with significant figures
If we look at the original measurements that went into the calculation, we see a length of 36.3 cm, which has three significant figures, and a height of 6.7 cm, which has two significant figures.
![Page 23: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/23.jpg)
Calculations with significant figures
Imagine there is a chain that is made of only two links, and one link is able to hold 3 kg before it breaks and the other is able to hold 2 kg, how much weight can the entire chain hold?
Strong enough to hold 3 kg
Strong enough to hold 2 kg
![Page 24: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/24.jpg)
Calculations with significant figures
If you are thinking that the chain could hold 5 kg (3 kg + 2 kg), then think again!
Strong enough to hold 3 kg
Strong enough to hold 2 kg
![Page 25: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/25.jpg)
Calculations with significant figures
If you are thinking that the chain could hold 5 kg (3 kg + 2 kg), then think again!
The chain would break at its weakest point. And so, as a whole, the chain would only be able to hold 2 kg before it broke.
Together only strong enough to hold 2 kg
![Page 26: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/26.jpg)
Calculations with significant figures
There is an old expression that says: “A chain is only as strong as its weakest link.”
![Page 27: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/27.jpg)
Calculations with significant figures
There is an old expression that says: “A chain is only as strong as its weakest link.”
If a chain were made of ten links, and nine of those links could hold 100 kg, but one could only hold 1 kg…
![Page 28: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/28.jpg)
Calculations with significant figures
How much weight would the entire chain be able to hold?
![Page 29: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/29.jpg)
Calculations with significant figures
How much weight would the entire chain be able to hold?
Just 1 kg!
![Page 30: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/30.jpg)
Calculations with significant figures
How much weight would the entire chain be able to hold?
Just 1 kg! Essentially, the one weak link ruins it for the rest of the links.
![Page 31: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/31.jpg)
Calculations with significant figures
The same holds true for calculations involving measurements. Consider the calculation below.
23.40 cm x 0.47 cm x 6.05 cm =
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
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Calculations with significant figures
The calculator answer has 6 significant figures.
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
![Page 33: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/33.jpg)
Calculations with significant figures
The calculator answer has 6 significant figures. But the weakest measurement has only 2 significant figures.
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
![Page 34: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/34.jpg)
Calculations with significant figures
The calculator answer has 6 significant figures. But the weakest measurement has only 2 significant figures. This means the answer must be rounded to only two significant figures:
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
67 cm3
![Page 35: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/35.jpg)
Calculations with significant figures
When you report an answer to be something like “66.5379 cm3”(just because that is what showed up on your calculator), you are claiming a level of precision much higher than the measurements deserve.
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
67 cm3
![Page 36: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/36.jpg)
Calculations with significant figures
An answer of 66.5379 cm3 means that the “66.537..” are definite, and only the “9” is a guess.
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
67 cm3
![Page 37: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/37.jpg)
Calculations with significant figures
An answer of 66.5379 cm3 means that the “66.537..” are definite, and only the “9” is a guess. But if the 0.47 cm could have just as easily been read as 0.46 cm, consider how different the answer would be.
23.40 cm x 0.47 cm x 6.05 cm = 66.5379 cm3
precise to 4 significant
figures
precise to 2 significant
figures
precise to 3 significant
figures
67 cm3
![Page 38: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/38.jpg)
Calculations with significant figures
So here is the rule:When multiplying or dividing two or more measurements, always round your answer off to the number of significant figures in the weakest measurement. (The weakest measurement is the one with the fewest significant figures)
![Page 39: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/39.jpg)
Calculations with significant figures
So here is the rule:When multiplying or dividing two or more measurements, always round your answer off to the number of significant figures in the weakest measurement. (The weakest measurement is the one with the fewest significant figures)
This ensures that your answer will not be any more or less precise than it should be.
![Page 40: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/40.jpg)
Calculations with significant figures
If crude measurements were made, then only crude values can be calculated from them. If more precise measurements were made, then more precise values can be calculated.
![Page 41: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/41.jpg)
Calculations with significant figures
So let’s say a student is calculating the average speed of a car as it traveled down the road.
![Page 42: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/42.jpg)
Calculations with significant figures
So let’s say a student is calculating the average speed of a car as it traveled down the road. Speed is distance divided by time.
![Page 43: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/43.jpg)
Calculations with significant figures
So let’s say a student is calculating the average speed of a car as it traveled down the road. Speed is distance divided by time. The student measures the time with a very precise stop watch and records a time of 146.39 s.
![Page 44: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/44.jpg)
Calculations with significant figures
So let’s say a student is calculating the average speed of a car as it traveled down the road. Speed is distance divided by time. The student measures the time with a very precise stop watch and records a time of 146.39 s. Distance is measured rather crudely: 680 m.
0 100 200 300 400 500 600 700 800m
![Page 45: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/45.jpg)
Calculations with significant figures
Speed = = =
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 46: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/46.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 47: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/47.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
This answer is what appears on the calculator, but it is obviously way too precise.
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 48: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/48.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
This answer is what appears on the calculator, but it is obviously way too precise.
What should it be rounded to?
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 49: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/49.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
The distance (680 m) has two significant figures
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 50: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/50.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
The distance (680 m) has two significant figures… and the time (146.39 s) has five significant figures.
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 51: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/51.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
The distance (680 m) has two significant figures… and the time (146.39 s) has five significant figures. The weaker measurement is the one with just two significant figures...
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 52: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/52.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
The distance (680 m) has two significant figures… and the time (146.39 s) has five significant figures. The weaker measurement is the one with just two significant figures… so the answer should be rounded to just two sig. figs.
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
![Page 53: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/53.jpg)
Calculations with significant figures
Speed = = = 4.645126033 m/s
The distance (680 m) has two significant figures… and the time (146.39 s) has five significant figures. The weaker measurement is the one with just two significant figures… so the answer should be rounded to just two sig. figs.
0 100 200 300 400 500 600 700 800m
distance time
680 m146.39 s
4.6 m/s
![Page 54: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/54.jpg)
Calculations with significant figures
Now try each of the following 20 problems.
![Page 55: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/55.jpg)
Calculations with significant figures
Now try each of the following 20 problems. Use a calculator, and then write your answer on paper.
![Page 56: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/56.jpg)
Calculations with significant figures
Now try each of the following 20 problems. Use a calculator, and then write your answer on paper. Make sure to round the answer to the correct number of significant figures…
![Page 57: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/57.jpg)
Calculations with significant figures
Now try each of the following 20 problems. Use a calculator, and then write your answer on paper. Make sure to round the answer to the correct number of significant figures…
…and also make sure to include correct units with each answer.
![Page 58: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/58.jpg)
Calculations with significant figures
1) 34.6 m x 14.8 m =
![Page 59: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/59.jpg)
Calculations with significant figures
1) 34.6 m x 14.8 m =
512 m2
![Page 60: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/60.jpg)
Calculations with significant figures
1) 34.6 m x 14.8 m =
512 m2
The 34.6 m and the 14.8 m both have three significant figures, so the answer is rounded to three significant figures.
![Page 61: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/61.jpg)
Calculations with significant figures
2) 67 cm x 38 cm =
![Page 62: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/62.jpg)
Calculations with significant figures
2) 67 cm x 38 cm =
2500 cm2
![Page 63: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/63.jpg)
Calculations with significant figures
2) 67 cm x 38 cm =
2500 cm2
The 67 cm and the 38 cm both have two significant figures, so the answer must be rounded to two significant figures.
![Page 64: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/64.jpg)
Calculations with significant figures
3) 0.0057 m x 0.0063 m =
![Page 65: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/65.jpg)
Calculations with significant figures
3) 0.0057 m x 0.0063 m =
0.000036 m2
![Page 66: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/66.jpg)
Calculations with significant figures
3) 0.0057 m x 0.0063 m =
0.000036 m2
The 0.0057 m and the 0.0063 m both have two significant figures, so the answer must be rounded to two significant figures.
![Page 67: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/67.jpg)
Calculations with significant figures
4) 34.0 mm x 72.7 mm =
![Page 68: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/68.jpg)
Calculations with significant figures
4) 34.0 mm x 72.7 mm =
2470 mm2
![Page 69: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/69.jpg)
Calculations with significant figures
4) 34.0 mm x 72.7 mm =
2470 mm2
The 34.0 mm and the 72.7 mm both have three significant figures, so the answer is rounded to three significant figures.
![Page 70: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/70.jpg)
Calculations with significant figures
5) 18.38 m x 23.54 m =
![Page 71: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/71.jpg)
Calculations with significant figures
5) 18.38 m x 23.54 m =
432.7 m2
![Page 72: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/72.jpg)
Calculations with significant figures
5) 18.38 m x 23.54 m =
432.7 m2
The 18.38 m and the 23.54 m both have four significant figures, so the answer is rounded to four significant figures.
![Page 73: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/73.jpg)
Calculations with significant figures
6) 207 m x 64 m =
![Page 74: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/74.jpg)
Calculations with significant figures
6) 207 m x 64 m =
13,000 m2
![Page 75: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/75.jpg)
Calculations with significant figures
6) 207 m x 64 m =
13,000 m2
The 207 m has three significant figures, but the 64 m has only two. Thus, the answer should be rounded to two significant figures.
![Page 76: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/76.jpg)
Calculations with significant figures
7) 296.3 cm x 0.8 cm =
![Page 77: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/77.jpg)
Calculations with significant figures
7) 296.3 cm x 0.8 cm =
200 cm2
![Page 78: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/78.jpg)
Calculations with significant figures
7) 296.3 cm x 0.8 cm =
200 cm2
The 296.3 cm has four significant figures, but the 0.8 cm only has one. Thus, the answer must be rounded to just one significant figure.
![Page 79: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/79.jpg)
Calculations with significant figures
8) 3.4 m x 16.3 m x 25.7 m =
![Page 80: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/80.jpg)
Calculations with significant figures
8) 3.4 m x 16.3 m x 25.7 m =
1400 m3
![Page 81: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/81.jpg)
Calculations with significant figures
8) 3.4 m x 16.3 m x 25.7 m =
1400 m3
The 3.4 m has two significant figures, and the 16.3 m and 25.7 m each have three significant figures. Thus, the answer is rounded to just two significant figure.
![Page 82: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/82.jpg)
Calculations with significant figures
9) 0.48 mL x 9.365 g/mL =
![Page 83: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/83.jpg)
Calculations with significant figures
9) 0.48 mL x 9.365 g/mL =
4.5 g
![Page 84: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/84.jpg)
Calculations with significant figures
9) 0.48 mL x 9.365 g/mL =
4.5 gThe 0.48 mL has two significant figures, and the 9.365 cm has four. Thus, the answer is rounded to just two significant figures.
![Page 85: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/85.jpg)
Calculations with significant figures
10) 25.50 m x 12.00 m =
![Page 86: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/86.jpg)
Calculations with significant figures
10) 25.50 m x 12.00 m =
306.0 m2
![Page 87: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/87.jpg)
Calculations with significant figures
10) 25.50 m x 12.00 m =
306.0 m2
The 25.50 m and the 12.00 m both have four significant figures, so the answer should have four significant figures. The calculator gives only “306” as the answer. In this situation, the answer must be enhanced up to four significant figures: “306.0”
![Page 88: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/88.jpg)
Calculations with significant figures
11) 17.5 km - 3.20 hr =
![Page 89: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/89.jpg)
Calculations with significant figures
11) 17.5 km - 3.20 hr =
5.47 km/hr
![Page 90: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/90.jpg)
Calculations with significant figures
11) 17.5 km - 3.20 hr =
5.47 km/hrThe 17.5 km and the 3.20 hr both have three significant figures, so the answer should have just three significant figures.
![Page 91: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/91.jpg)
Calculations with significant figures
12) 234.53 g - 85 mL =
![Page 92: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/92.jpg)
Calculations with significant figures
12) 234.53 g - 85 mL =
2.8 g/mL
![Page 93: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/93.jpg)
Calculations with significant figures
12) 234.53 g - 85 mL =
2.8 g/mLThe 234.53 g has five significant figures, but the 85 mL has only two. Thus, the answer should have only two significant figures.
![Page 94: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/94.jpg)
Calculations with significant figures
13) 2300 m2 - 725 m =
![Page 95: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/95.jpg)
Calculations with significant figures
13) 2300 m2 - 725 m =
3.2 m
![Page 96: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/96.jpg)
Calculations with significant figures
13) 2300 m2 - 725 m =
3.2 mThe 2300 m2 has two significant figures and the 725 m has three. The answer should therefore be rounded to just two significant figures.
![Page 97: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/97.jpg)
Calculations with significant figures
14) 17.5 km - 3.50 hr =
![Page 98: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/98.jpg)
Calculations with significant figures
14) 17.5 km - 3.50 hr =
5.00 km/hr
![Page 99: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/99.jpg)
Calculations with significant figures
14) 17.5 km - 3.50 hr =
5.00 km/hrThe 17.5 km and the 3.50 hr both have three significant figures, so the answer should have three significant figures. The calculator gives an answer of simply “5.” So this “5” must be enhanced up to three significant figures: “5.00.”
![Page 100: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/100.jpg)
Calculations with significant figures
15) 32.0 m3 – 7.0 m =
![Page 101: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/101.jpg)
Calculations with significant figures
15) 32.0 m3 – 7.0 m =
4.6 m2
![Page 102: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/102.jpg)
Calculations with significant figures
15) 32.0 m3 – 7.0 m =
4.6 m2
The 32.0 m3 has three significant figures, but the 7.0 m has only two, so the answer should be rounded to just two significant figures.
![Page 103: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/103.jpg)
Calculations with significant figures
16) 679.0 g – 678.9 mL =
![Page 104: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/104.jpg)
Calculations with significant figures
16) 679.0 g – 678.9 mL =
1.000 g/mL
![Page 105: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/105.jpg)
Calculations with significant figures
16) 679.0 g – 678.9 mL =
1.000 g/mLThe 679.0 g and the 678.9 mL both have four significant figures, so the answer should be rounded to four significant figures.
![Page 106: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/106.jpg)
Calculations with significant figures
17) (65 m x 17 m) – 4.83 s =
![Page 107: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/107.jpg)
Calculations with significant figures
17) (65 m x 17 m) – 4.83 s =
230 m2/s
![Page 108: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/108.jpg)
Calculations with significant figures
17) (65 m x 17 m) – 4.83 s =
230 m2/s
The 65 m and 17 m both have two significant figures, and the 4.83 s has three significant figures. Thus the answer should have two significant figures.
![Page 109: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/109.jpg)
Calculations with significant figures
18) 56.94 g – (3.42 cm x 7.61 cm x 0.35 cm) =
![Page 110: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/110.jpg)
Calculations with significant figures
18) 56.94 g – (3.42 cm x 7.61 cm x 0.35 cm) =
6.3 g/cm3
![Page 111: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/111.jpg)
Calculations with significant figures
18) 56.94 g – (3.42 cm x 7.61 cm x 0.35 cm) =
6.3 g/cm3
The 56.94 g has four significant figures, the 3.42 cm and the 7.61 cm each have three significant figures, but the 0.35 cm has only two significant figures. The answer therefore should be rounded to just two significant figures.
![Page 112: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/112.jpg)
Calculations with significant figures
19) 215 cm x 372 cm =
![Page 113: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/113.jpg)
Calculations with significant figures
19) 215 cm x 372 cm =
80,000 cm2
![Page 114: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/114.jpg)
Calculations with significant figures
19) 215 cm x 372 cm =
80,000 cm2
The 215 cm and the 372 cm both have three significant figures, so the answer should be rounded to three significant figures. 79,980 rounds up to 80,000, which appears to have only one significant figure. A line over the second 0 fixes this problem.
![Page 115: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/115.jpg)
Calculations with significant figures
20) 2.480 m – 0.124 s =
![Page 116: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/116.jpg)
Calculations with significant figures
20) 2.480 m – 0.124 s =
20.0 m/s
![Page 117: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/117.jpg)
Calculations with significant figures
20) 2.480 m – 0.124 s =
20.0 m/sThe 2.480 m has four significant figures and the 0.124 s has three, so the answer should have three significant figures. The calculator gives an answer of “20”, which has only one significant figure. It must be enhanced to three significant figures: 20.0.
![Page 118: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/118.jpg)
Calculations with significant figures
So… How many did you get correct?
![Page 119: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/119.jpg)
Calculations with significant figures
So… How many did you get correct?
Hopefully this tutorial program has helped you understand how to round off answers for these sort of calculations
![Page 120: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/120.jpg)
Calculations with significant figures
It is important to remember that this rule of rounding answers off to the fewest number of significant figures applies only to multiplication and division.
![Page 121: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/121.jpg)
Calculations with significant figures
It is important to remember that this rule of rounding answers off to the fewest number of significant figures applies only to multiplication and division.
There is a different rule that is used for adding and subtracting...
![Page 122: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/122.jpg)
Calculations with significant figures
It is important to remember that this rule of rounding answers off to the fewest number of significant figures applies only to multiplication and division.
There is a different rule that is used for adding and subtracting… and that will be the topic of our next tutorial.
![Page 123: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/123.jpg)
Calculations with significant figures
So now you know what to do when you multiply and divide measured quantities:
![Page 124: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/124.jpg)
Calculations with significant figures
So now you know what to do when you multiply and divide measured quantities: simply round your answer off to the same number of significant figures as there are in the weakest measurement
![Page 125: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/125.jpg)
Calculations with significant figures
So now you know what to do when you multiply and divide measured quantities: simply round your answer off to the same number of significant figures as there are in the weakest measurement (weakest meaning fewest number of significant figures).
![Page 126: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/126.jpg)
Calculations with significant figures
So now you know what to do when you multiply and divide measured quantities: simply round your answer off to the same number of significant figures as there are in the weakest measurement (weakest meaning fewest number of significant figures). But do addition and subtraction follow the same rule?
![Page 127: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/127.jpg)
Calculations with significant figures
So now you know what to do when you multiply and divide measured quantities: simply round your answer off to the same number of significant figures as there are in the weakest measurement (weakest meaning fewest number of significant figures). But do addition and subtraction follow the same rule? Not quite.
![Page 128: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/128.jpg)
Calculations with significant figures
In adding and subtracting, you still look for the weakest measurement, but weak is defined differently.
![Page 129: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/129.jpg)
Calculations with significant figures
In adding and subtracting, you still look for the weakest measurement, but weak is defined differently. You don’t count significant figures at all.
![Page 130: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/130.jpg)
Calculations with significant figures
In adding and subtracting, you still look for the weakest measurement, but weak is defined differently. You don’t count significant figures at all. Instead, you look at what place the guess (the last significant figure) is in.
![Page 131: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/131.jpg)
Calculations with significant figures
For example, in 138.4 g, the guess is the “4” and it is in the tenths place.
.,ten-thousands place
thousands place
hundreds place
tens place
hundredths place
thousandths place
ten-thousandths place
1 0 0 0 0 0 0 0 0ones place
tenths place
![Page 132: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/132.jpg)
Calculations with significant figures
For example, in 138.4 g, the guess is the “4” and it is in the tenths place.
In 0.281 g, the guess is the “1” and it is in the thousandths place.
.,ten-thousands place
thousands place
hundreds place
tens place
hundredths place
thousandths place
ten-thousandths place
1 0 0 0 0 0 0 0 0ones place
tenths place
![Page 133: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/133.jpg)
Calculations with significant figures
For example, in 138.4 g, the guess is the “4” and it is in the tenths place.
In 0.281 g, the guess is the “1” and it is in the thousandths place. Between these two measurements, 138.4 g is the weaker measurement, because its guess is in the higher place.
.,ten-thousands place
thousands place
hundreds place
tens place
hundredths place
thousandths place
ten-thousandths place
1 0 0 0 0 0 0 0 0ones place
tenths place
![Page 134: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/134.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
![Page 135: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/135.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
This is what the calculator would give as the answer.
![Page 136: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/136.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
This is what the calculator would give as the answer. But it should be rounded at the highest guessed place (the tenths place) .
![Page 137: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/137.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
This is what the calculator would give as the answer. But it should be rounded at the highest guessed place (the tenths place) .
Which would change it to…
![Page 138: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/138.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.7 g
This is what the calculator would give as the answer. But it should be rounded at the highest guessed place (the tenths place) .
Which would change it to…
![Page 139: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/139.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The reason is this: starting at the left-hand side of the calculator answer:
![Page 140: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/140.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The reason is this: starting at the left-hand side of the calculator answer: The “1” in the hundreds place is definite because it comes from the definite “1” above it.
![Page 141: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/141.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The reason is this: starting at the left-hand side of the calculator answer: The “1” in the hundreds place is definite because it comes from the definite “1” above it.
![Page 142: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/142.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place.
![Page 143: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/143.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place.
![Page 144: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/144.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place.
![Page 145: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/145.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place.
![Page 146: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/146.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place…
![Page 147: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/147.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place… It came from adding a definite “2” from 0.281 to a guessed “4” from 138.4.
![Page 148: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/148.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place… It came from adding a definite “2” from 0.281 to a guessed “4” from 138.4. If the “4” could have been read as a “3” instead, that would have changed the “6” to a “5.”
![Page 149: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/149.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.3 g
+ 0.281 g
138.581 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place… It came from adding a definite “2” from 0.281 to a guessed “4” from 138.4. If the “4” could have been read as a “3” instead, that would have changed the “6” to a “5.”
![Page 150: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/150.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place… It came from adding a definite “2” from 0.281 to a guessed “4” from 138.4. If the “4” could have been read as a “3” instead, that would have changed the “6” to a “5.” This “6” therefore cannot be considered definite.
![Page 151: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/151.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 g
The same holds true for the “3” in the tens place. And for the “8” in the ones place. But think about the “6” in the tenths place… It came from adding a definite “2” from 0.281 to a guessed “4” from 138.4. If the “4” could have been read as a “3” instead, that would have changed the “6” to a “5.” This “6” therefore cannot be considered definite. And if the “6” is indefinite (guessed), then the answer has to end there.
![Page 152: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/152.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.681 gSince the “6” is followed by an “8,” it rounds up, giving us…
![Page 153: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/153.jpg)
Calculations with significant figures
And if these two measurements were added together:
138.4 g
+ 0.281 g
138.7 gSince the “6” is followed by an “8,” it rounds up, giving us…
![Page 154: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/154.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
![Page 155: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/155.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm
![Page 156: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/156.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm This is the calculator answer,
![Page 157: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/157.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm This is the calculator answer, but let’s consider where the guesses are.
![Page 158: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/158.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm This is the calculator answer, but let’s consider where the guesses are. The “6” in “315,600 cm” is in the hundreds place and the “9” in “219 cm” is in the ones place.
![Page 159: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/159.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm This is the calculator answer, but let’s consider where the guesses are. The “6” in “315,600 cm” is in the hundreds place and the “9” in “219 cm” is in the ones place. Since we have to round the answer off at the highest guessed place (the hundreds place),
![Page 160: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/160.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,819 cm This is the calculator answer, but let’s consider where the guesses are. The “6” in “315,600 cm” is in the hundreds place and the “9” in “219 cm” is in the ones place. Since we have to round the answer off at the highest guessed place (the hundreds place), the answer becomes…
![Page 161: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/161.jpg)
Calculations with significant figures
Let’s try another problem:
315,600 cm
+ 219 cm
315,800 cm This is the calculator answer, but let’s consider where the guesses are. The “6” in “315,600 cm” is in the hundreds place and the “9” in “219 cm” is in the ones place. Since we have to round the answer off at the highest guessed place (the hundreds place), the answer becomes…
![Page 162: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/162.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
![Page 163: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/163.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
The fact that there are three numbers being added together does not change anything.
![Page 164: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/164.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
![Page 165: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/165.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
Again, this is the calculator answer,
![Page 166: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/166.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
Again, this is the calculator answer, but let’s consider the guesses:
![Page 167: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/167.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
Again, this is the calculator answer, but let’s consider the guesses:
The “5” (in the hundredths place), the “8” (in the thousandths place) and the “6” (in the tenths place) are the three guesses.
![Page 168: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/168.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
Again, this is the calculator answer, but let’s consider the guesses:
The “5” (in the hundredths place), the “8” (in the thousandths place) and the “6” (in the tenths place) are the three guesses.
The highest guessed place is the tenths place so this is where the answer needs to be rounded.
![Page 169: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/169.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.3748 s
Again, this is the calculator answer, but let’s consider the guesses:
The “5” (in the hundredths place), the “8” (in the thousandths place) and the “6” (in the tenths place) are the three guesses.
The highest guessed place is the tenths place so this is where the answer needs to be rounded. This gives and answer of…
![Page 170: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/170.jpg)
Calculations with significant figures
Let’s try another problem:
34.75 s
0.0248 s
+ 112.6 s
147.4 s
Again, this is the calculator answer, but let’s consider the guesses:
The “5” (in the hundredths place), the “8” (in the thousandths place) and the “6” (in the tenths place) are the three guesses.
The highest guessed place is the tenths place so this is where the answer needs to be rounded. This gives and answer of…
![Page 171: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/171.jpg)
Calculations with significant figures
Let’s try word problem:
![Page 172: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/172.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg.
![Page 173: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/173.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat.
![Page 174: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/174.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg.
![Page 175: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/175.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
![Page 176: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/176.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
The set-up for this problem would look like this:
![Page 177: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/177.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
The set-up for this problem would look like this:
And the calculator answer would be:
![Page 178: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/178.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000.038 kg
The set-up for this problem would look like this:
And the calculator answer would be:
![Page 179: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/179.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000.038 kg
But let’s consider where the guesses are:
![Page 180: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/180.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000.038 kg
But let’s consider where the guesses are:
The “7” (in the thousands place), and the “8” (in the thousandths place) are the two guesses.
![Page 181: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/181.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000.038 kg
But let’s consider where the guesses are:
The “7” (in the thousands place), and the “8” (in the thousandths place) are the two guesses.
The highest guessed place is clearly the thousands place…
![Page 182: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/182.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000.038 kg
But let’s consider where the guesses are:
The “7” (in the thousands place), and the “8” (in the thousandths place) are the two guesses.
The highest guessed place is clearly the thousands place…
So the answer rounds to…
![Page 183: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/183.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000 kg
But let’s consider where the guesses are:
The “7” (in the thousands place), and the “8” (in the thousandths place) are the two guesses.
The highest guessed place is clearly the thousands place…
So the answer rounds to…
![Page 184: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/184.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000 kg
This might seem strange at first:
![Page 185: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/185.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000 kg
This might seem strange at first: we started with 197,000 kg, added something to it and ended up with the same mass: 197,000 kg.
![Page 186: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/186.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000 kg
This might seem strange at first: we started with 197,000 kg, added something to it and ended up with the same mass: 197,000 kg. But this should make sense since what we are adding is so tiny.
![Page 187: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/187.jpg)
Calculations with significant figures
Let’s try word problem:
A construction crane weighs 197,000 kg. The crane operator sticks his chewed gum under the seat. The gum weighs 0.038 kg. How much does the crane weigh now?
197,000 kg
+ 0.038 kg
197,000 kg
This might seem strange at first: we started with 197,000 kg, added something to it and ended up with the same mass: 197,000 kg. But this should make sense since what we are adding is so tiny.
When a bucket-full of water has one more drop added to it… it’s still just a bucket-full of water!
![Page 188: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/188.jpg)
Calculations with significant figures
How about subtraction:
![Page 189: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/189.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s.
![Page 190: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/190.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time.
![Page 191: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/191.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
![Page 192: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/192.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
The set-up for this problem would look like this:
![Page 193: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/193.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
The set-up for this problem would look like this:
And the calculator answer would be…
![Page 194: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/194.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.23 s
The set-up for this problem would look like this:
And the calculator answer would be…
![Page 195: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/195.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.23 s
But let’s consider where the guesses are:
![Page 196: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/196.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.23 s
But let’s consider where the guesses are:
The “3” (in the hundredths place) and the “2” (in the tenths place) are our two guesses.
![Page 197: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/197.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.23 s
But let’s consider where the guesses are:
The “3” (in the hundredths place) and the “2” (in the tenths place) are our two guesses.
The highest guessed place is the tenths place
![Page 198: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/198.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.23 s
But let’s consider where the guesses are:
The “3” (in the hundredths place) and the “2” (in the tenths place) are our two guesses.
The highest guessed place is the tenths place so that is where our answer should be rounded. Giving us…
![Page 199: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/199.jpg)
Calculations with significant figures
How about subtraction:
Joey’s best time in the 200 m was 21.43 s. He buys new shoes guaranteed to shave 0.2 s off his time. With the new shoes, what should his best time be?
21.43 s
- 0.2 s
21.2 s
But let’s consider where the guesses are:
The “3” (in the hundredths place) and the “2” (in the tenths place) are our two guesses.
The highest guessed place is the tenths place so that is where our answer should be rounded. Giving us…
![Page 200: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/200.jpg)
Calculations with significant figures
Now try each of the following 10 problems.
![Page 201: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/201.jpg)
Calculations with significant figures
Now try each of the following 10 problems. Use a calculator, and then write your answer on paper. Make sure to round the answer at the correct place…
![Page 202: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/202.jpg)
Calculations with significant figures
Now try each of the following 10 problems. Use a calculator, and then write your answer on paper. Make sure to round the answer at the correct place…
…and also make sure to include correct units with each answer.
![Page 203: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/203.jpg)
Calculations with significant figures
1) 18.543 cm + 2.61 cm =
![Page 204: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/204.jpg)
Calculations with significant figures
1) 18.543 cm + 2.61 cm =
21.15 cm
![Page 205: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/205.jpg)
Calculations with significant figures
1) 18.543 cm + 2.61 cm =
21.15 cm
The guesses are the “3” (in the thousandths place) and the “1” (in the hundredths place), so the answer must be rounded at the hundredths place.
![Page 206: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/206.jpg)
Calculations with significant figures
1) 18.543 cm + 2.61 cm =
21.15 cm
Note that the units simply match the units in the two measurements being added. That is always the case for addition and subtraction.
![Page 207: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/207.jpg)
Calculations with significant figures
2) 285 g – 17 g =
![Page 208: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/208.jpg)
Calculations with significant figures
2) 285 g – 17 g =
268 g
![Page 209: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/209.jpg)
Calculations with significant figures
2) 285 g – 17 g =
268 g
The guesses are the “5” (in the ones place) and the “7” (also in the ones place), so the answer must be rounded at the ones place.
![Page 210: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/210.jpg)
Calculations with significant figures
2) 285 g – 17 g =
268 g
Actually, the calculator answer already ended in the ones place, so no rounding was really necessary.
![Page 211: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/211.jpg)
Calculations with significant figures
2) 285 g – 17 g =
268 g
Actually, the calculator answer already ended in the ones place, so no rounding was really necessary. That happens quite often in addition and subtraction: the calculator answer just happens to be the correct answer!
![Page 212: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/212.jpg)
Calculations with significant figures
3) 7.5 m + 11.42 m + 6.3 m =
![Page 213: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/213.jpg)
Calculations with significant figures
3) 7.5 m + 11.42 m + 6.3 m =
25.2 m
![Page 214: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/214.jpg)
Calculations with significant figures
3) 7.5 m + 11.42 m + 6.3 m =
25.2 m
The guesses are the “5” (in the tenths place), the “2” (in the hundredths place) and the “3” (in the tenths place), so the answer must be rounded at the tenths place.
![Page 215: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/215.jpg)
Calculations with significant figures
4) 124.58 mg – 122.9 mg =
![Page 216: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/216.jpg)
Calculations with significant figures
4) 124.58 mg – 122.9 mg =
1.7 mg
![Page 217: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/217.jpg)
Calculations with significant figures
4) 124.58 mg – 122.9 mg =
1.7 mg
The guesses are the “8” (in the hundredths place), the “9” (in the tenths place), so the answer must be rounded at the tenths place.
![Page 218: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/218.jpg)
Calculations with significant figures
5) 6.45 g + 9.32 g =
![Page 219: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/219.jpg)
Calculations with significant figures
5) 6.45 g + 9.32 g =
15.77 g
![Page 220: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/220.jpg)
Calculations with significant figures
5) 6.45 g + 9.32 g =
15.77 g
The guesses are the “5” (in the hundredths place) and the “2” (also in the hundredths place).
![Page 221: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/221.jpg)
Calculations with significant figures
5) 6.45 g + 9.32 g =
15.77 g
The guesses are the “5” (in the hundredths place) and the “2” (also in the hundredths place). The calculator answer already ends in the hundredths place so it is correct as it is.
![Page 222: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/222.jpg)
Calculations with significant figures
6) 165.4 L – 138.4 L =
![Page 223: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/223.jpg)
Calculations with significant figures
6) 165.4 L – 138.4 L =
27.0 L
![Page 224: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/224.jpg)
Calculations with significant figures
6) 165.4 L – 138.4 L =
27.0 L
The guesses are the “4” (in the tenths place) and the other “4” (also in the tenths place). So the answer should end in the tenths place.
![Page 225: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/225.jpg)
Calculations with significant figures
6) 165.4 L – 138.4 L =
27.0 L
The guesses are the “4” (in the tenths place) and the other “4” (also in the tenths place). So the answer should end in the tenths place.
The calculator just gives “27” as an answer, so here you have to enhance it up to “27.0”
![Page 226: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/226.jpg)
Calculations with significant figures
7) 130 g + 200 g + 489 g
![Page 227: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/227.jpg)
Calculations with significant figures
7) 130 g + 200 g + 489 g
800 g
![Page 228: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/228.jpg)
Calculations with significant figures
7) 130 g + 200 g + 489 g
800 g
The guesses are the “3” (in the tens place), the “2” (in the hundreds place) and the “9” (in the ones place). So the answer should end in the hundreds place.
![Page 229: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/229.jpg)
Calculations with significant figures
8) 130 g + 200 g + 489 g
![Page 230: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/230.jpg)
Calculations with significant figures
8) 130 g + 200 g + 489 g
820 g
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Calculations with significant figures
8) 130 g + 200 g + 489 g
820 g
The guesses are the “3” (in the tens place), the “0” (in the tens place) and the “9” (in the ones place). So the answer should end in the tens place this time.
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Calculations with significant figures
9) 61.7 cm x 9.2 cm =
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Calculations with significant figures
9) 61.7 cm x 9.2 cm =
570 cm2
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Calculations with significant figures
9) 61.7 cm x 9.2 cm =
570 cm2
This is a multiplication problem, and follows a different rule. Don’t look for where the guesses are. Just count how many significant figures there are in each measurement. (Remember???)
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Calculations with significant figures
9) 61.7 cm x 9.2 cm =
570 cm2
The 61.7 cm has three significant figures, and the 9.2 cm has just two. Thus, the answer is rounded to just two significant figure.
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Calculations with significant figures
10) 553 cm + 16.87 cm =
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Calculations with significant figures
10) 553 cm + 16.87 cm =
570 cm
![Page 238: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/238.jpg)
Calculations with significant figures
10) 553 cm + 16.87 cm =
570 cm
The guesses are the “3” (in the ones place) and the “7” (in the hundredths place). So the answer should end in the ones place.
![Page 239: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/239.jpg)
Calculations with significant figures
10) 553 cm + 16.87 cm =
570 cm
The calculator gives an answer of “569.87.” The “9” would round up to give an answer of “570,” but this appears to end in the tens place. To show the “0” is significant, we put a line over it.
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Calculations with significant figures
Well, hopefully these tutorials have proved helpful in teaching you how to round answers when you are doing calculations with measurements:
![Page 241: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/241.jpg)
Calculations with significant figures
Well, hopefully these tutorials have proved helpful in teaching you how to round answers when you are doing calculations with measurements:
-- When multiplying and dividing, always round your answer off to the fewest number of significant figures.
![Page 242: Calculations with significant figures So now you know how to determine the number of significant figures in a number and how to round numbers off, what.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649cfe5503460f949cf120/html5/thumbnails/242.jpg)
Calculations with significant figures
Well, hopefully these tutorials have proved helpful in teaching you how to round answers when you are doing calculations with measurements:
-- When multiplying and dividing, always round your answer off to the fewest number of significant figures.
-- When adding and subtracting, always round your answer off at the highest guessed place.