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 the
initial 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 in
measurements 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 least
precise 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
Question For Thought
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.
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.
4.5 cm
2 significant
figures
Uncertain
4.54 cm
3 significant
figures
More certain
due to greater
precision
Significant figures are necessary to reduce
uncertainty in our measurements.
Significant figures indicate the
precision of the measured value!!