Rules for Counting Significant Figures
1. Nonzero Integers – Nonzero integers always count as significant figures.
2. Zeros – There are three classes of zeros:
a. Leading Zeros are zeros that precede all nonzero digits. These do not count as significant
figures. In the number 0.00057 the four zeros simply indicate the position of the decimal point.
This number has only two significant figures.
b. Captive zeros are zeros between nonzero digits. These always count as significant figures. The
number 540.0005 has four captive zeros, all of which are significant. Therefore there are seven
significant figures in the number.
c. Trailing zeros are zeros at the right end of the number. They are significant only if the number
contains a decimal point. The number 36000 has only two significant figures. The number
36000. has five significant figures. The number 3.6000 x 104 has five significant figures.
3. Exact Numbers – Many times calculations involve numbers that were not obtained using measuring
devices, but were determined by counting: 10 fingers, 4 sheets of paper, 20 desks, etc. Such numbers
are called exact numbers. They can be assumed to have an infinite number of significant figures. Other
examples of exact numbers are the 2 in 2r. Exact numbers can also arise from definitions. For
example, one inch is defined as exactly 2.54 centimeters. Thus in the statement, 1 in=2.54cm, neither
the 2.54 nor the 1 limits the number of significant figures when used in a calculation.
1
Rules For Significant Figures In Mathematical Operations
1. For Multiplication and division the number of significant figures in the result is the same as the
number of significant figures in that measurement used to obtain the result that has the smallest (or
smaller, if only two numbers are involved) number of significant figures in it.
Example 1:
4800 / 300.0 = 16
2 sig figs
2 sig. figs.
4 sig. figs.
Example 2:
0.000400 x 35.000 = 0.0140
3 sig figs
5 sig figs
3 sig figs
2. For addition or subtraction the result has the same number of decimal places as the least precise
measurement used in the calculation. Stated in another way, the result will have the same
uncertainty as that measurement with the largest uncertainty.
Example 1:
15.773
100.23
+
1.4
117.403
Uncertainty
0.001
0.01
0.1
Largest uncertainty in the tenths place
117.4
corrected answer
Example 2:
23400
- 490.
22910
100 Uncertainty in the hundreds place
1
Uncertainty in the units place
22900 Uncertainty in the hundreds place
Corrected answer
2