Significant Figures: The Rules (With Examples)

Significant figures are the digits in a number that actually carry meaningful information about its precision. The rules come down to which zeros count and which don't. In short: non-zero digits always count, zeros between non-zeros count, leading zeros never count, and trailing zeros count only when there's a decimal point. Let's make that concrete, and you can check any number with our free significant figures calculator.

The rules

Non-zero digits are always significant. 472 has three significant figures.
Captive zeros (zeros between non-zero digits) are always significant. 1002 has four.
Leading zeros (zeros before the first non-zero digit) are never significant. 0.0032 has only two.
Trailing zeros with a decimal point are significant. 2.500 has four.
Trailing zeros without a decimal point are ambiguous. 1500 might have two, three, or four — scientific notation removes the doubt.

Counting examples

Run a few numbers through the rules and the pattern sticks: 472 has three sig figs, 1002 has four (the captive zeros count), 0.0032 has two (the leading zeros don't), and 2.500 has four (the trailing zeros count because of the decimal point). Writing an ambiguous number like 1500 as 1.5 x 10^3 makes its precision unmistakable — that's two sig figs.

Rounding to a set number of sig figs

To round to a chosen number of significant figures, keep that many significant digits and round the rest away. Rounding 3.14159 to three sig figs gives 3.14, and rounding it to two gives 3.1. Count from the first non-zero digit, not from the decimal point.

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Sig figs in calculations

Two quick rules govern most lab and science work. For multiplication and division, your answer should have as many significant figures as the least precise number you used. For addition and subtraction, the answer should have as many decimal places as the term with the fewest decimal places. These conventions vary a little by course and instructor, so follow whatever your class requires.

Check your figures fast

When you need to count or round significant figures quickly, use the significant figures calculator, and for very large or very small numbers the scientific notation converter keeps the precision clear. To have the rules explained in plain language, COSMIQ's free voice tutor is free for every learner.

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