Rules for Counting Significant Figures

  1. Nonzero Integers – Nonzero integers always count as significant figures.
  1. Zeros – There are three classes of zeros:
  2. 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.
  1. 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.
  1. 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.
  1. 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.

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 figs5 sig figs3 sig figs

  1. 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:

Uncertainty

15.7730.001

100.230.01

+ 1.40.1Largest uncertainty in the tenths place

117.403

117.4

corrected answer

Example 2:

23400100 Uncertainty in the hundreds place

- 490.1 Uncertainty in the units place

22910

22900 Uncertainty in the hundreds place

Corrected answer

1