Significant figures calculator
This significant figures calculator counts the sig figs in a number, rounds a number to the sig figs you choose, and does arithmetic with the sig fig rules. It explains which digits count and why.
- Counts decimals, whole numbers and scientific notation
- Rounds to any number of sig figs
- Add, subtract, multiply and divide with the right precision
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How to use the significant figures calculator
- Choose Count to find how many sig figs a number has, Round to round it, or Calculate to add, subtract, multiply or divide two measurements.
- Type the number exactly as written, keeping every zero. Scientific notation works as 6.02e23 or 6.02 × 10^23.
- For rounding, enter how many significant figures you want. Tick the even-digit box if your course rounds a lone 5 to the even digit.
- Read the answer and the rule applied to each digit or step.
The significant figures rules
Start at the first nonzero digit on the left and count it and every digit to its right, with one exception for trailing zeros.
- Nonzero digits are always significant: 482 has 3.
- Zeros between nonzero digits (captive zeros) are significant: 70.607 has 5.
- Leading zeros are never significant; they only place the decimal point: 0.0032 has 2.
- Trailing zeros after a decimal point are significant: 2.50 has 3, and 0.004050 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous; assume they are not significant. 1300 has 2, while 1300. and 1.300 × 10³ have 4.
× and ÷: round to the fewest significant figures + and −: round to the fewest decimal places
Worked example
Multiply 4.56 by 1.4.
- 4.56 has 3 significant figures; 1.4 has 2.
- Exact product: 4.56 × 1.4 = 6.384.
- Round to 2 significant figures, the fewer of the two: 6.384 → 6.4.
Adding instead: 12.11 + 18.0 = 30.11. 12.11 has two decimal places and 18.0 has one, so the sum is rounded to one decimal place: 30.1.
Sig fig examples
| Number | Sig figs | Why |
|---|---|---|
| 0.01 | 1 | The leading zeros only place the decimal point |
| 0.005 | 1 | Only the 5 counts |
| 0.0010 | 2 | The trailing zero after the 1 is significant |
| 0.0015 | 2 | 1 and 5 |
| 100 | 1 | Trailing zeros, no decimal point (ambiguous: 1 to 3) |
| 1000 | 1 | Ambiguous: 1 to 4; write 1.000 × 10³ for 4 |
| 100.0 | 4 | The decimal point makes every zero count |
| 6.022 × 10²³ | 4 | Only the digits before × 10 count |
Rounding to significant figures
Look at the first digit you are dropping. Less than 5: leave the last kept digit alone. More than 5, or 5 followed by any nonzero digit: round up. Exactly 5 with nothing after it: most classes round up, while some chemistry textbooks, including OpenStax Chemistry, round to whichever choice makes the last digit even (92.85 → 92.8).
Round only once, at the end. In a multi-step problem, carry at least one extra digit through the steps so rounding errors do not build up. 0.9999 to 3 significant figures is 1.00: rounding up carries through every 9.
Common questions
How do you count significant figures?
Start at the first nonzero digit and count it and every digit after it. Leading zeros never count; trailing zeros count only when there is a decimal point. 0.004050 has 4 significant figures.
Is 0.01 one or two significant figures?
One. The zeros before the 1 are leading zeros that only place the decimal point. 0.010 would have two, because a trailing zero after a decimal point is significant.
How many significant figures does 1000 have?
As written, 1, because trailing zeros without a decimal point are ambiguous and are assumed not significant. Write 1000. or 1.000 × 10³ to show 4 significant figures.
What is 0.9999 to 3 significant figures?
1.00. The fourth digit is 9, so the third 9 rounds up, which carries through to make 1.00. Keep both zeros to show three significant figures.
What are the sig fig rules for addition and subtraction?
Round the answer to the fewest decimal places among the numbers. 1.0023 g + 4.383 g = 5.3853 g, rounded to 5.385 g because 4.383 has three decimal places.
What are the sig fig rules for multiplication and division?
Round the answer to the fewest significant figures among the numbers. 0.6238 cm × 6.6 cm = 4.11708 cm², rounded to 4.1 cm² because 6.6 has two significant figures.
Sources
- OpenStax Chemistry 2e, 1.5 Measurement Uncertainty, Accuracy, and Precision. Counting rules for leading, captive and trailing zeros; addition/subtraction and multiplication/division rules; round-half-to-even for a dropped 5
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