Mathematics
Significant figures calculator
Type a number: each digit is coloured by the rule that applies to it, with the count of significant figures and rounding to as many figures as you choose.
The rules for significant figures
Significant figures are the digits that carry information about a measurement. Every non-zero digit is significant, and so are zeros between two non-zero digits: 305 has three.
Leading zeros never are: they only place the decimal point, so 0.00405 has three significant figures. Trailing zeros after the decimal point always are, because someone wrote them on purpose: 4.050 has four. Trailing zeros of a whole number with no point, as in 1200, are ambiguous; scientific notation settles it: 1.20 × 10³ has three.
To round to n figures, look at the next digit: 5 or more rounds up. In calculations, the result of a multiplication or division should not have more significant figures than the least precise input.
Common mistakes
- Counting leading zeros: 0.0045 has two significant figures, not five.
- Dropping trailing zeros after the point: 2.50 and 2.5 do not say the same thing about precision.
- Reporting a result with every digit the calculator shows, more precise than the data it came from.
Frequently asked questions
How many significant figures does 100 have?
One to three: without more information there is no telling. 1 × 10², 1.0 × 10² and 1.00 × 10² have one, two and three.
Do zeros in the middle count?
Yes: a zero between two non-zero digits is always significant, as in 1005 (four figures).
How do you round 2.675 to three figures?
Look at the fourth digit, 5: round up to get 2.68. The calculator works on the digits as written, free of floating-point errors.
How this calculation works
The number is read digit by digit. The first non-zero digit is found: those before it are leading zeros. Every digit from there on is significant, except the trailing zeros of a whole number written without a decimal separator, which are marked ambiguous. Rounding works on the digit sequence, half up, with a carry that may add a digit and raise the exponent.