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Significant Figures Calculator
Count the significant figures in a measurement, or round a number to the number of significant figures you need. Leading zeros, captive zeros and trailing zeros are treated by the standard rules.
The counting rules
Significant figures are the digits in a measurement that carry information about its precision. Five rules cover nearly every case:
- Every non-zero digit is significant.
- Zeros between non-zero digits are significant (1002 has four).
- Leading zeros, which only locate the decimal point, are not significant (0.0012 has two).
- Trailing zeros after a decimal point are significant (2.500 has four).
- Trailing zeros in a whole number without a decimal point are ambiguous. They are usually treated as placeholders, so 1500 has two significant figures unless a marker says otherwise.
Scientific notation removes the ambiguity, because every digit in the coefficient counts: 1.50 × 103 has three, and 1.500 × 103 has four. Exact counts, such as 12 eggs, and defined constants, such as 100 cm in a metre, have unlimited significant figures.
Worked counting examples
| Number | Sig figs | Reason |
|---|---|---|
| 0.004050 | 4 | 4, 0, 5 and the trailing 0 after the point |
| 1002 | 4 | Zeros between non-zero digits count |
| 1500 | 2 | Trailing zeros without a point are placeholders |
| 1500. | 4 | The point marks the zeros as measured |
| 1.20e3 | 3 | All coefficient digits count |
| 0.0012 | 2 | Leading zeros do not count |
Rounding to a number of significant figures
To round to N significant figures, find the first non-zero digit, keep N digits from there, and look at the next digit. If it is 5 or more, increase the last kept digit by one; otherwise leave it. Rounding 0.0045678 to three figures gives 0.00457, and rounding 123,456 to three figures gives 123,000. A carry can change the digit count: 9.996 to three figures becomes 10.0, because the 9s roll over. This page works on the typed digits directly, not on a floating-point value, so it is not affected by binary representation errors. Compare the decimal-place version in the rounding calculator.
Significant figures in calculations
When measured values are combined, the answer cannot be more precise than the least precise input. For multiplication and division, round the result to the smallest number of significant figures among the inputs. For addition and subtraction, round to the fewest decimal places instead. Keep extra digits in intermediate steps and round only at the end, otherwise small rounding errors add up. As a quick example, 2.5 m × 3.14 m has the answer 7.85 m², but with only two significant figures in 2.5 the reported area should be 7.9 m². These are conventions for reporting, not a replacement for a proper uncertainty analysis, and some courses or journals ask for different treatment. For very large or small values see the scientific notation calculator.
Worked example
Count the significant figures in 0.004050. The zeros after the decimal point and before the 4 are leading zeros, while the final zero is a trailing zero after the decimal point.
Inputs
| Task | Count the significant figures |
|---|---|
| Number | 0.004050 |
Result
Counted digits: 4 0 5 0
| Number | 0.004050 |
|---|---|
| Significant figures | 4 |
| Counted digits | 4050 |
| Same value in scientific notation | 4.050 × 10^-3 |
| Why | A decimal point is present, so every digit from the first non-zero digit onward counts, including trailing zeros. |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How many significant figures does 0.004050 have?
It has four: the 4, the 0 between 4 and 5, the 5, and the trailing 0 after the decimal point. The leading zeros before the 4 only place the decimal point.
Are trailing zeros significant?
They are significant when the number has a decimal point, as in 2.500. In a whole number such as 1500 they are ambiguous and usually not counted unless a decimal point or scientific notation shows otherwise.
How do I round to three significant figures?
Keep the first three digits starting from the first non-zero digit, then round up if the next digit is 5 or more. For example, 0.0045678 becomes 0.00457.
Why does 9.996 round to 10.0 and not 9.99?
Rounding 9.996 up carries through the 9s and gives 10.0. The result still shows exactly three significant figures, with the trailing zero kept.
Do exact numbers have significant figures?
Exact counts and defined conversion factors have unlimited significant figures, so they never limit the precision of a calculated answer.
Related calculators
References and sources
- IUPAC Compendium of Chemical Terminology (the Gold Book): entries on significant figures and precision. Link
- NIST Guide for the Use of the International System of Units (SI), Special Publication 811, on rounding and expressing values.