Significant Figures and Rounding

Enter the number as text

This tool rounds a decimal without first converting it to binary floating point. The value 1.005 is therefore an exact tie when rounded to two decimal places and gives 1.01. Exact ties round away from zero, so negative 2.5 rounds to negative 3 as an integer. Significant figure results use scientific notation and preserve trailing zeros. Plain decimal notation is also shown when it preserves the intended precision unambiguously. In the formulas, q is the rounding increment, n is the number of significant figures and d is the number of decimal places.

Counting written digits

Leading zeros are ignored. Every digit from the first nonzero digit onward counts, so 0.00120 has three significant figures. Trailing zeros in integers can be ambiguous. Here they count as written: 1200 means four figures while 1.2e3 means two. Zero is reported with a count of 0 because its precision cannot be determined from the text alone. The maximum target is 100 figures or decimal places. This arithmetic does not establish measurement uncertainty or the quality of a measurement.

Decide which digits to retain

Suppose you round 0.006785 to three significant figures. Starting with the first nonzero digit, retain 6, 7 and 8. The next digit is 5, so increase the last retained digit to obtain 0.00679. Leading zeros do not increase the figure count. The input contains four significant figures, while the result is reported with three. To run this example, enter 0.006785 in the number field as decimal point machine input. A decimal comma is only for localized explanatory text.

Decimal places and significant figures express different requirements. Decimal places fix a position to the right of the decimal separator. Significant figures determine how many digits to retain relative to the magnitude. Decide which requirement applies to your measurement report first. In successive calculations, retain the full available value and round at the reporting stage instead of repeatedly rounding intermediate results. Writing more digits does not improve a measurement's accuracy. Trailing zeros may deliberately communicate precision, so preserve them when copying a result. The tool rounds written digits. Calibration, instrument resolution and the uncertainty budget require separate consideration.

Frequently asked questions

How many significant figures are in 0.00450?

For example, the written value 0.00450 has 3 significant figures, because leading zeros do not count while the final zero after the nonzero digits does. This count follows the entered decimal text, so numerically equal values can carry different written precision. It does not establish measurement uncertainty or instrument accuracy.

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