Starter 1.How would you record the following measurements? How many sig figs? a.b. 2.Count the sig...
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Transcript of Starter 1.How would you record the following measurements? How many sig figs? a.b. 2.Count the sig...
Starter1. How would you record the following measurements? How many
sig figs?a. b.
2. Count the sig figs in the following measured values:a. 0.0004050b. 1890c. 1890.090d. 6.930 x 106
mL
inches
Starter Answers1. How would you record the following measurements? How many
sig figs?a. b.
2. Count the sig figs in the following measured values:a. 0.0004050 4 sig figsb. 1890 3 sig figsc. 1890.090 7 sig figsd. 6.930 x 106 4 sig figs
4.98 mL3 sig figs
8.24 in3 sig figs
mL
inchesYour last digit might be different!
Arithmetic with Significant Figures
Arithmetic with sig figs!
Sometimes we need to use our measured values in calculations. Here are some examples:
hwlVolume
mmmMassAve
VVVolumeDisplacedt
ds
V
md
fi
3
)(. 321
When you do arithmetic, you need to figure out how many sig figs your answer should have. This will depend on the sig figs in your measurements.
Remember, your measurements might have been made with different amounts of precision. This is reflected by the number of sig figs.
Low precision in one measurement will limit the precision of your answer.
Arithmetic with sig figs!
ExampleLet’s say you wanted to calculate the density of a liquid. To do this, you found the volume using a beaker. The volume was 55 mL. Then, you used an analytical balance to measure the mass. The mass was 55.1345 g.
mL
g
V
md
55
1345.55
How precise is the answer?How many sig figs should I record?
6 sig figs
2 sig figs
1.0 g/mL
2 sig figs
Multiplication and DivisionThe general rule for multiplication and division is that your answer must have only as many sig figs as the least precise measurement.
Example2 sig figs
4 sig figs
13 m3
Round to2 sig figs
mmmhwlVolume 56.4335.22.1
3 sig figs
More Example
4200.800
500012.012465
0123.0465.3
More Example
194200.800
3500012.012465
2820123.0465.3
4 sig figs 3 sig figs 3 sig figs
3 sig figs 2 sig figs 2 sig figs 1 sig fig
2 sig figs5 sig figs
1 sig fig
2 sig figs
Addition and SubtractionThe rules for addition and subtraction are different. For addition and subtraction the answer must be rounded to the least number of decimal places from any of the terms.
mLmLVolumeDisplaced 1.801.14
2 decimal places
1 decimal placeRound to1 decimal place
5.9 mL
Examples
02.0341.97
0.401.0
2.112
152.083.9
Answers
32.9702.0341.97
0.40.401.0
112.112
98.9152.083.9
2 decimal places 3 decimal places
2 decimal places
0 decimal places 1 decimal place
0 decimal places
2 decimal places 1 decimal place
1 decimal place
3 decimal places 2 decimal places2 decimal places