How to use the Significant Figures
- Type the number as it appears in your data, including trailing zeros.
- Read the significant-figure count.
- Set the precision you want to round to.
- Use the scientific form when trailing-zero ambiguity needs removing.
How the calculation works
The counting rules are: all non-zero digits count; zeros between non-zero digits count; leading zeros never count; and trailing zeros count only when a decimal point is present. So 0.004520 has four significant figures — the leading zeros are placeholders, the trailing zero is a measured digit — while 4520 written without a decimal point is ambiguous, conventionally read as three.
That ambiguity is precisely why scientific notation is preferred in reporting: 4.52 × 10³ and 4.520 × 10³ are unambiguously three and four significant figures. If your data is ambiguous, converting it is the only reliable fix.
Propagation rules differ by operation. Multiplication and division give a result with as many significant figures as the least precise input. Addition and subtraction instead match the least precise decimal place, not the sig-fig count — adding 12.11 to 0.3 gives 12.4, not 12.41. Exact counts and defined constants have unlimited significant figures and never limit the result.
Multiplication/division: match the fewest sig figs ; addition/subtraction: match the fewest decimal placesSource: ISO 80000-1 rounding guidance; standard significant-figure conventions in measurement science.
Worked example
A rectangle measured as 12.11 cm by 0.30 cm — reporting the area correctly.
- 12.11 has four sig figs; 0.30 has two.
- Raw product: 3.633 cm².
- Multiplication limits the result to two sig figs.
3.6 cm² — reporting 3.633 would claim precision the ruler never had.
Frequently asked questions
Do trailing zeros always count?+
Only when a decimal point is present. 4520 is ambiguous; 4520. or 4.520 × 10³ is not.
How many sig figs does an exact count have?+
Unlimited. Counting 12 items is exact and never limits the precision of a result.
Should I round at every step?+
No. Carry full precision through and round once at the end, then report to the correct sig figs.
Why do addition and multiplication use different rules?+
Addition is limited by absolute precision (decimal places); multiplication is limited by relative precision (sig figs).
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.