Significant Figures

(Or How many decimal places should I keep?)

In physics, all experimental measurements have some uncertainty involved.  The accuracy of any measurement is expressed by the number of significant digits written when the measurement is reported. 

There are several rules for determining the number of significant digits (or significant figures) in a measurement.  In general significant figures are determined starting with the leftmost digit.

1. All non-zero digits are significant.
2. The leftmost nonzero digit is the first or most significant figure.  For example, in the number 0.02340, the first significant figure is the 2.
3. If there is a decimal point, the rightmost digit is the last or least significant figure.  For example, in 0.02340 the first two zeros from the left are not significant but the zero after the 4 is significant.
4. If there is no decimal point explicitly shown, the rightmost non-zero digit is the least significant figure.  For example, in 3400 the 4 is the least significant figure since neither zero is significant in this case.
5. All digits between the most significant figure and the least significant figure are significant.  For example, 6.07 has three significant figures.

The general rule of thumb in this class is that calculated results can have no more than 3 significant figures (sig figs).  This usually means that results shown on a calculator must be rounded off to 3 sig figs.  

For example, 252,194,701 would be rounded to 252,000,000.

Sometimes more or fewer than 3 sig figs would be allowed according to the following rules:

MULTIPLICATION or DIVISION

• Keep the same number of sig figs as the factor with the least number of sig figs.

Example: 1.2 x 4.56 = 5.472 on the calculator.  But since the one factor has only 2 sig figs, the answer must be rounded to 2 sig figs or 5.5.

ADDITION or SUBTRACTION

• Keep the same number of decimal places as the factor with the least amount.

Example: 1.234 + 5.67 = 6.904 on the calculator.  But since the one factor has only 2 decimal places, so must the answer.  Thus the result must be rounded to 6.90 (where the zero is significant.  See rule 3 above.)

For more information, questions, or comments, please call Steve Platte at (602)787-6646 or send e-mail to steve.platte@pvmail.maricopa.edu

31 January 2000