What are significant figures?
Significant figures are the digits that carry meaning about how precisely a number was measured. A length of 1.200 km has four: writing the zeros says they were measured. In the answer, the digits that count are in bold and the ones that don't are grey and crossed out.
Source NIST Guide to the SI (SP 811) · Chapter 7, section 7.9: which digits are significant ↗
How to count significant figures
NIST’s rules: leading zeros don't count, zeros between other digits do, and final zeros count only after a decimal point. That is why 34.0 has three significant figures but 340 has two.
Here it is with your numbers:
- The leading zeros (0.00) only show where the decimal point is, so they don't count.
- The digits 4, 9 and 2 aren't zero, so they count.
- The final zero comes after a decimal point, so it counts.
- That makes 4 significant figures.
- To round to 2 significant figures, keep 4 and 9 and look at the next digit, 2: below 5, so the last kept digit stays. That gives 0.0049.
It means 0.004920 is given to 4 significant figures. Rounded to 2, it is 0.0049.
A lone 5 can be rounded two ways. Rounding it up is what most classes and spreadsheets do. Some laboratories round it to the even digit instead, so that rounding doesn't push results up over time: 3.450 becomes 3.4 but 3.550 becomes 3.6.
Source NIST Special Publication 1038 · significant digits (footnote 7, page 5) and rounding (section 4.4.1.1) ↗NIST GLP 9 (2019) · Rounding: even/odd and spreadsheet rounding ↗
Your number rounded to each number of significant figures
| Figures | Rounded | Scientific notation |
|---|---|---|
| 1 | 0.005 | 5 × 10⁻³ |
| 2 | 0.0049 | 4.9 × 10⁻³ |
| 3 | 0.00492 | 4.92 × 10⁻³ |
| 4 | 0.004920 | 4.920 × 10⁻³ |
Significant figures examples
FAQs
What are significant figures?
Significant figures, also called significant digits, are the digits needed to show a number to the precision it was measured. Leading zeros like the ones in 0.00492 only place the decimal point, so they are not significant.
Source NIST Guide to the SI (SP 811) · Chapter 7, section 7.9: which digits are significant ↗
How do you count significant figures?
Count every digit except leading zeros, and except the final zeros of a whole number with no decimal point. Zeros between other digits count, and zeros at the end after a decimal point count. So 30.4, 34.0 and 3.40 each have three, but 340 has two.
How many significant figures are in 100?
100 has one significant figure. Final zeros in a whole number written without a decimal point are not counted. If those zeros were measured, write 1.00 × 10² to show three significant figures.
Sources
- NIST Special Publication 1038: significant digits (footnote 7, page 5) and rounding (section 4.4.1.1)
- NIST Guide to the SI (SP 811): Chapter 7, section 7.9: which digits are significant
- NIST GLP 9 (2019): Rounding: even/odd and spreadsheet rounding