Significant figures calculator
Count the significant figures in a number, and round it to the number you need.
Scientific notation works too, like 1.20e3.
The rules in short
Every nonzero digit counts. Zeros between nonzero digits count. Leading zeros never count, since they only place the decimal point. Trailing zeros count only when the number has a decimal point.
So 0.004050 has four significant figures, 100. has three, and 100 on its own has one. Check your instructor’s convention for whole numbers that end in zeros.
Worked examples
Counting. 0.00450 has 3 significant figures (leading zeros don’t count, the trailing zero after the decimal does). 105.0 has 4 (zeros between digits count, and so does the final zero after the decimal). 1200 has 2 as written, because trailing zeros with no decimal point are ambiguous; write 1.200 × 10³ to show 4.
Multiplying and dividing: keep the fewest significant figures of any number used. 4.56 × 1.4 = 6.384, which rounds to 6.4 (2 sig figs, from 1.4).
Adding and subtracting: keep the fewest decimal places. 12.11 + 18.0 + 1.013 = 31.123, which rounds to 31.1 (one decimal place, from 18.0).
Frequently asked questions
Do exact numbers limit significant figures?
No. Counted values (12 eggs) and defined conversions (1 m = 100 cm) are exact and have unlimited significant figures, so they never limit your answer.
Why are trailing zeros sometimes not significant?
In a number like 1200 there is no way to tell whether the zeros were measured or are just placeholders. A decimal point (1200.) or scientific notation (1.20 × 10³) removes the doubt.
When should I round in a multi-step problem?
Keep extra digits in your calculator through every step and round only the final answer. Rounding along the way builds up rounding error.
How do significant figures work in scientific notation?
Only the digits in the front part count. 6.022 × 10²³ has 4 significant figures; the power of ten just sets the size.