Cup of coffee = ~ 200 ml Add drop of H 2 O = 0.05 mL New volume: ~200 mL or 200.05 mL?? If you say...
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Transcript of Cup of coffee = ~ 200 ml Add drop of H 2 O = 0.05 mL New volume: ~200 mL or 200.05 mL?? If you say...
Cup of coffee = ~ 200 ml
Add drop of H2O = 0.05 mL
New volume:~200 mL or 200.05 mL??
If you say 200.05 you imply that the volume of theinitial cup of coffee was exactly 200 mL and we don’t know that accurately.
New volume:~200 mL or 200.05 mL??
We convey our uncertainty in measured quantities by abiding by the rules of significant figures.
Definition of Significant figures.The number of all known digits reported inmeasurements plus one estimated digits.
We would have to report the coffee measurement as ~200 because that is our least accurate number.
A chain can never be stronger than its weakest link.
An answer can never be more precise than the leastprecise number you use to get the answer.
Significant Figures
Try These!
1.36 3 significant digits
172 3 significant digits
3247 4 significant digits
Try These!
0.5 1 significant digit
0.0053567 5 significant digits
0.0008769 4 significant digits
Try These!
20.05 4 significant digits
1.003 4 significant digits
102001 6 significant digits
Try These!
9.000000000 10 significant digits
85.00 4 significant digits
9.98000 6 significant digits
Try These!
250 2 significant digits
780,000,000 2 significant digits
90. 2 significant digits
Practice
46800
3 significant figures
Rule:Trailing zeroes in a number with no decimal
are not significant
Practice
126.48
5 significant figures
Rule:All nonzero integers are significant
Practice
1.0005
5 significant figures
Rule:Captive zeroes are always significant
Practice
90.0
3 significant figures
Rules:1. Trailing zeroes in a decimal number are
significant.
2. Zeroes at the end of a number count if there is a written decimal point.
Practice
192
3 significant figures
Rule:All nonzero integers are significant
Practice
0.000004
1 significant figure
Rule:Leading zeroes are never significant
Practice
0.01006
4 significant figures
Rules:1.Leading zeroes are never significant 2.Captive zeroes are always significant
Using two different rulers, I measured the width of my hand to be 4.5 centimeters and 4.54 centimeters. Explain the difference between these two measurements.
Question For Thought
The first measurement implies that my hand is somewhere between 4.5 and 4.9 cm long. There is a uncertainty in this number because we have to estimate.
The second measurement implies that my hand is between 4.5 and 4.6 cm long. This measurement is more certain due to its greater precision.
Significant figures are necessary to reduceuncertainty in our measurements.
Significant figures indicate the precision of the measured value!!
4.5 cm2 significant
figuresUncertain
4.54 cm3 significant
figures
More certain due to greater
precision