OneTaskBy Tim King · Updated
Significant Figures Calculator
Count Sig Figs and Round to N Significant Figures
OneTask is free, with no sign-up, and built by one person.
If this tool saved you time, a coffee helps keep new ones coming.
How the Significant Figures Calculator works
This significant figures calculator counts the sig figs in any number you type and rounds it to the number of significant figures you choose. The result appears in plain form, in scientific notation and in E notation, with a note when trailing zeros make the count ambiguous, as in 1500.
Significant figures are the digits that carry real information about a measurement's precision. Leading zeros only place the decimal point, so 0.0045 has two. Zeros between other digits always count, and trailing zeros count when there is a decimal point. A whole number such as 1500 is the awkward case: it could have two, three or four significant figures, which is why science writes it as 1.5 × 10³ or 1.50 × 10³ to remove the doubt.
How the significant figures calculator works
The formula for rounding to n significant figures is to find the first non-zero digit, count n digits from there and round the last kept digit using half up. Digits before the decimal point that are dropped become zeros, so the size of the number is kept. Scientific notation moves the point to just after the first significant digit.
First example. 0.004560 has 4 significant figures: the leading zeros do not count, but the final zero does because it follows a decimal point.
Second example. 123456 to 3 significant figures is 123000, which is 1.23 × 10⁵ or 1.23E5 in calculator notation.
How many significant figures does 100.0 have? Four. The trailing zeros sit after a decimal point, so they record a measured precision.
Counting significant figures in common examples
| Number | Significant figures | Why |
|---|---|---|
| 123 | 3 | All non-zero digits count |
| 1.23 | 3 | All non-zero digits count |
| 0.0123 | 3 | Leading zeros never count |
| 100 | 1 | Trailing zeros without a point are ambiguous |
| 100. | 3 | All non-zero digits count |
| 100.0 | 4 | Trailing zeros after a point count |
| 1.00 × 10^2 | 3 | Only the digits before the exponent count |
| 0.00500 | 3 | Leading zeros never count |
| 5.020 | 4 | Trailing zeros after a point count |
| 1002 | 4 | Zeros between non-zero digits count |
| 0.1 | 1 | Leading zeros never count |
| 0.10 | 2 | Leading zeros never count |
| 7 | 1 | All non-zero digits count |
| 70 | 1 | Trailing zeros without a point are ambiguous |
| 7.0 | 2 | Trailing zeros after a point count |
| 70.0 | 3 | Trailing zeros after a point count |
| 6.022e23 | 4 | Only the digits before the exponent count |
| 0.000300 | 3 | Leading zeros never count |
| 40506 | 5 | Zeros between non-zero digits count |
| 3.1416 | 5 | All non-zero digits count |
| 2500 | 2 | Trailing zeros without a point are ambiguous |
| 2.500 | 4 | Trailing zeros after a point count |
| 0.05040 | 4 | Leading zeros never count |
| 9.80 | 3 | Trailing zeros after a point count |
Tips and pitfalls
- Leading zeros never count. 0.00072 has two significant figures, the 7 and the 2.
- Write the decimal point. 20. or 20.0 shows the trailing zero was measured; plain 20 is ambiguous.
- Exact numbers are unlimited. Counted items and defined constants, such as 12 in a dozen, do not limit precision.
- Multiply by the fewest. In multiplication and division, round the answer to the fewest significant figures among the inputs.
FAQ
How do you count significant figures?
Start at the first non-zero digit and count every digit to the end, including zeros in between. Trailing zeros count only if the number has a decimal point. So 3.0040 has five, 0.025 has two and 4,500 has two, three or four depending on intent.
Do trailing zeros count as significant figures?
They count when the number has a decimal point, as in 2.50 or 300.0, because someone chose to write them. In a whole number such as 300 they are ambiguous. Scientific notation settles it: 3.00 × 10² clearly has three significant figures.
How do you round to 3 significant figures?
Find the first non-zero digit, keep three digits from there and round the third using the next one. So 0.0045678 becomes 0.00457 and 98,765 becomes 98,800. The calculator does this for any count from one up to the number's full length.
What is the difference between decimal places and significant figures?
Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.00123 has five decimal places but three significant figures. Use the rounding calculator when you need a fixed number of decimal places.
How many significant figures should my answer have?
For multiplying or dividing, match the input with the fewest significant figures. For adding or subtracting, match the fewest decimal places instead. Keep extra digits during the working and only round the final answer, so the error does not grow.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
Related tools
Rounding Calculator
Round to decimal places or the nearest 10, with five rounding rules.
Scientific Notation Converter
Convert numbers to scientific, E and engineering notation and back.
Scientific Calculator
Trig, logs, powers, factorials and memory, in one expression.
Exponent Calculator
Raise a number to any power, with exact results for big powers.
Decimal To Fraction Calculator
Decimals to simplified fractions, recurring decimals and inch fractions included.