Significant figures are the digits in a number that carry actual meaning about the precision of a measurement.

Identifying Significant Figures

In physics, not all digits in a measurement are equally important. Significant figures tell us how precise our tool was. Follow these basic rules to identify them:

• Non-zero digits: All numbers from 1 to 9 are always significant. For example, 45.6 has three significant figures.
• Zeros between numbers: Zeros trapped between two non-zero digits are always significant. In 5002, there are four significant figures.
• Leading zeros: Zeros to the left of the first non-zero digit are never significant. In 0.007, there is only one significant figure.
• Trailing zeros: Zeros at the end of a number are significant only if there is a decimal point. The number 500 has one significant figure, but 500.0 has four.

The Rules of Rounding

Rounding helps us keep our final answer as accurate as the least precise measurement used. If you are calculating a result, use these simple steps:

• Look at the digit immediately to the right of the one you are keeping.
• If that digit is less than 5, keep the last digit the same. For example, 4.34 becomes 4.3.
• If the digit is 5 or greater, increase the last digit by one. For example, 4.36 becomes 4.4.

Calculations and Precision

When you multiply or divide numbers, your final answer should have the same number of significant figures as the measurement with the fewest significant figures. If you measure a length of 2.5 cm (two figures) and multiply it by 4.22 cm (three figures), your calculator gives 10.55. Because 2.5 is the least precise, you round your result to 11 (two significant figures). When adding or subtracting, look at the decimal places instead. The answer must have the same number of digits after the decimal as the measurement with the fewest decimal places.