The rules for counting significant figures
- Nonzero digits always count. 4.56 has 3.
- Zeros between nonzero digits count. 1,005 has 4.
- Leading zeros never count. They only place the decimal point: 0.0045 has 2.
- Trailing zeros count if there's a decimal point. 0.00450 has 3, and 12.0 has 3.
- Trailing zeros in a whole number without a decimal point are ambiguous. 1200 could have 2, 3 or 4. The usual rule counts 2. Write 1200. (with a point) for 4, or use scientific notation: 1.20 × 10³ has 3.
In scientific notation every digit of the number in front counts, so it removes the ambiguity.
Sig figs in calculations
× and ÷: keep the fewest significant figures of any input
+ and −: round to the least precise decimal place of any input
+ and −: round to the least precise decimal place of any input
- 2.5 × 3.42 = 8.55. 2.5 has 2 sig figs, so the answer is 8.6.
- 12.11 + 18.0 = 30.11. 18.0 is only known to the tenths place, so the answer is 30.1.
- 1,200 + 3.5 = 1,203.5. 1,200 is known to the hundreds place, so the answer is 1,200.
When a result is a tie, like 8.55 to 2 sig figs, this calculator rounds half up, the rule most textbooks use. Some labs round half to even instead; the rounding calculator does both.
When this doesn't apply
- Exact numbers have unlimited significant figures: counted items (3 beakers), defined values (1 inch = 2.54 cm exactly) and pure numbers in formulas (the 2 in 2πr). Don't let them limit your answer.
- In a calculation with several steps, keep extra digits along the way and round only the final answer.
- Sig figs are a quick way to show precision. Lab work with stated uncertainties (like ± 0.02 g) uses error propagation instead.