Significant Figures Calculator and Rounder
Every nonzero digit is significant, zeros between them are significant, leading zeros are not, and trailing zeros count only after a decimal point. So 0.004560 has 4 significant figures: 4, 5, 6 and the final 0.
Type it exactly as written: 1.50 and 1.5 have different significant figures.
0.004560
- Significant
- Not significant
Significant figures
4
Scientific notation
4.560 × 10⁻³
Rounded to 2
0.0046
Rounded, scientific
4.6 × 10⁻³
Show the math
- 1
Find the significant digits
0.004560 → 4, 5, 6, 0
Leading zeros only place the decimal point, so they never count. Trailing zeros after a decimal point count: they show the measurement's precision.
= 4 significant figures
Read the steps as text
- Find the significant digits. 0.004560 → 4, 5, 6, 0 Leading zeros only place the decimal point, so they never count. Trailing zeros after a decimal point count: they show the measurement's precision.
- Write it in scientific notation. 0.004560 = 4.560 × 10⁻³ Scientific notation keeps exactly the significant digits, so there's no ambiguity.
- Round to 2 significant figures. Keep 45, next digit is 6 → round up → 46 Look at the first digit you drop: 5 or more rounds the last kept digit up, 4 or less leaves it.
The rules for significant figures
Significant figures are the digits that carry meaning about a measurement's precision. Nonzero digits always count. Zeros between nonzero digits always count, so 1002 has 4. Leading zeros never count, because they only place the decimal point: 0.0045 has 2.
Trailing zeros are the tricky case. After a decimal point they count, because writing 3.0 instead of 3 says the measurement is precise to a tenth. In a whole number with no decimal point, like 1500, they're ambiguous: the zeros might be measured or might just be placeholders. The calculator counts 1500 as 2 significant figures and flags the ambiguity. Writing 1.50 × 10³ or 1500. (with a trailing point) removes it.
Rounding to significant figures
To round, keep the required number of digits starting from the first nonzero one, then look at the next digit: 5 or more rounds the last kept digit up, 4 or less leaves it alone. 0.0045678 to 3 significant figures is 0.00457.
The calculator rounds the decimal digits exactly as you typed them, so it doesn't suffer from the binary rounding errors that make some software round 2.675 down to 2.67. It also shows the result in scientific notation, which is the clearest way to show exactly how many figures are significant.
Frequently asked questions
- How many significant figures does 100 have?
- One, by the usual convention, since trailing zeros in a whole number without a decimal point aren't counted. If all three digits are measured, write it as 100. or 1.00 × 10².
- Are zeros after a decimal point significant?
- Trailing zeros after a decimal point are significant (2.50 has 3), but leading zeros are not (0.025 has 2).
- How many significant figures should my answer have?
- When multiplying or dividing, round to the fewest significant figures in any of the inputs. When adding or subtracting, round to the fewest decimal places instead.
- Do exact numbers limit significant figures?
- No. Counted quantities and defined values, like 12 eggs in a dozen or 100 cm in a meter, are exact and have unlimited significant figures.