Sig Fig Calculator
Count significant figures in any number, including scientific notation, and round to N sig figs, with the rule for every digit spelled out one at a time.
Sig Fig Calculator: with the default inputs, significant figures is 4.
Typed exactly as written — trailing zeros and a trailing decimal point both matter.
- The significant digits
- 4050
- In scientific notation
Written with exactly the significant digits counted above.
- 4.050 × 10⁻³
- Decimal places
What the addition and subtraction rule counts.
- 6
- Rounded
- 0.0041
- Rounded, in scientific notation
- 4.1 × 10⁻³
Assumptions
- Trailing zeros in a whole number written without a decimal point are treated as not significant (the common textbook convention) and flagged as ambiguous.
- Rounding is round-half-up (away from zero) on the digits as typed; some labs use round-half-to-even instead.
- A number made only of zeros is reported as having no significant figures.
| # | Digit | Place value | Significant? | Rule |
|---|---|---|---|---|
| 1 | 0 | 10⁰ | No | Leading zero — only a placeholder, never significant |
| 2 | 0 | 10⁻¹ | No | Leading zero — only a placeholder, never significant |
| 3 | 0 | 10⁻² | No | Leading zero — only a placeholder, never significant |
| 4 | 4 | 10⁻³ | Yes | Non-zero digit — always significant |
| 5 | 0 | 10⁻⁴ | Yes | Zero between non-zero digits — always significant |
| 6 | 5 | 10⁻⁵ | Yes | Non-zero digit — always significant |
| 7 | 0 | 10⁻⁶ | Yes | Trailing zero with a decimal point — significant |
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits always count | 4.56 | 3 |
| Zeros between non-zero digits count | 1005 | 4 |
| Leading zeros never count | 0.0072 | 2 |
| Trailing zeros after a decimal point count | 2.500 | 4 |
| Trailing zeros in a whole number are ambiguous | 1200 (or 1200. for 4) | 2 |
| In scientific notation, count the mantissa | 6.020 × 10²³ | 4 |
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How this is worked out
The formula
Count: every non-zero digit + zeros between them + trailing zeros when a decimal point is written Not counted: leading zeros; trailing zeros of a whole number with no decimal point (ambiguous) Round to n s.f.: keep the first n significant digits; if digit n+1 is 5 or more, add 1 to digit n Multiplying/dividing: answer has the fewest sig figs of the inputs. Adding/subtracting: the fewest decimal places.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Number
- Typed exactly as written — trailing zeros and a trailing decimal point both matter.up to 60 characters · defaults to "0.004050"
- Round to this many significant figures
- A number.from 1 to 30 · whole numbers only · defaults to 2
What you get back
- Significant figuresmain answer
- The significant digits
- In scientific notation
- Written with exactly the significant digits counted above.
- Decimal places
- What the addition and subtraction rule counts.
- Rounded
- Rounded, in scientific notation
What this assumes
- Trailing zeros in a whole number written without a decimal point are treated as not significant (the common textbook convention) and flagged as ambiguous.
- Rounding is round-half-up (away from zero) on the digits as typed; some labs use round-half-to-even instead.
- A number made only of zeros is reported as having no significant figures.
About this calculator
Significant figures are the digits in a measurement that carry real information — every digit you are sure of, plus the first uncertain one. This sig fig calculator counts them in any number you type, including scientific notation, and rounds the number to however many significant figures you need, with the rule for every single digit written out in a table.
How to use it
Type the number exactly as it was written, because the notation is the information. 2.5 and 2.500 are the same value but not the same measurement: the second claims precision to the thousandth. A trailing decimal point matters as well — 1200 has two significant figures by convention, while "1200." has four. Scientific notation works as 6.02e23 or 6.02 × 10^23. Then set how many figures to round to.
The rules
- Non-zero digits always count: 4.56 has three.
- Zeros between non-zero digits ("captive" zeros) always count: 1005 has four.
- Leading zeros never count — they only place the decimal point: 0.0072 has two.
- Trailing zeros after a decimal point count: 2.500 has four.
- Trailing zeros in a whole number with no decimal point are ambiguous. 1200 could have two, three or four. The standard convention, which this calculator follows, counts two and flags the number as ambiguous; to remove the doubt, write 1.200 × 10³.
- Scientific notation counts only the mantissa: 6.020 × 10²³ has four.
Rounding to significant figures
Keep the first n significant digits, then look at the next one: 5 or more rounds the last kept digit up, anything less leaves it. The rounding is done on the digits exactly as you typed them, never on a floating-point approximation, so 0.00405 rounds to 0.0041 as it should rather than drifting to 0.0040. When a rounded whole number ends in placeholder zeros (1995 to three figures is 2000), the result is also given in scientific notation, 2.00 × 10³, because only that form shows all three figures.
When to use which rule in calculations
Multiplying or dividing, the answer keeps as many significant figures as the least precise input. Adding or subtracting, it keeps as many decimal places as the input with the fewest — which is why the decimal places are reported too. Round only the final answer, not each intermediate step.
Exact numbers
Counted quantities (12 eggs) and defined constants (100 cm in a metre) are exact and have unlimited significant figures. They never limit the precision of a result.
Frequently asked questions
▸How many significant figures does 0.004050 have?
Four: 4, 0, 5 and the final 0. The three leading zeros only place the decimal point; the zero between 4 and 5 is captive, and the trailing zero after a decimal point is measured.
▸Are trailing zeros significant?
After a decimal point, yes — 2.50 has three. In a whole number without a decimal point, such as 1200, they are ambiguous and conventionally not counted. Write 1200. or 1.200 × 10³ to show they are measured.
▸How do you round to 3 significant figures?
Find the first non-zero digit, count three digits from it, and look at the fourth: 5 or more rounds the third up. So 0.0045678 becomes 0.00457 and 98,765 becomes 98,800.
▸How do sig figs work in scientific notation?
Every digit in the mantissa is significant and the power of ten is not. 3.00 × 10⁸ has three significant figures, the same as 300. would.
▸Does zero have significant figures?
Not in the usual sense, because the rules are defined by the non-zero digits. Report a measured zero with its decimal places instead, such as 0.00 g.
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