Significant Figures Calculator
Add, subtract, multiply, or divide with significant figures. See each input's sig figs, the exact result, and the correctly rounded reported value.
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What are significant figures?
Significant figures capture how precisely a number is known. When you calculate with measured values, the answer cannot be more precise than the least precise input — so the result is rounded to the right number of significant figures.
Counting rules
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros are never significant (0.007 has 1).
- Trailing zeros are significant only with a decimal point (380.0 has 4; 78800 has 3; 78800. has 5).
Tip: Writing a trailing zero after a decimal point is a promise: 2.00 means you measured to the hundredths, so it carries three significant figures.
The two calculation rules
- Add / subtract — keep the least precise decimal place. 7 + 0.063 = 7.063 → reported as 7 (ones place).
- Multiply / divide — keep the fewest significant figures. 2 × 2.35 = 4.7 → reported as 5 (1 sig fig).
They differ because sums are limited by absolute precision (place value) while products are limited by relative precision (sig figs).
Worked examples
- 7.1 + 0.063 = 7.163 → least precise place is the tenths → 7.2.
- 81 × 26.2 = 2122.2 → fewest sig figs is 2 → 2100.
- 343 ÷ 52 = 6.596… → fewest sig figs is 2 → 6.6.
- 2.00 × 2.35 = 4.7 → three sig figs → 4.70.
Common mistakes
- Using the wrong rule — decimal places for +/−, sig figs for ×/÷.
- Dropping a significant trailing zero (reporting 4.7 instead of 4.70).
- Treating exact counts as if they limit precision.
To express a rounded result compactly, use scientific notation; to round to a plain place value use rounding numbers.
Frequently asked questions
- How do you count significant figures?
- All non-zero digits are significant. Zeros between them are significant. Leading zeros are never significant. Trailing zeros are significant only if there is a decimal point — so 380.0 has 4 sig figs, 78800 has 3, and 78800. (with a trailing dot) has 5.
- What is the sig fig rule for adding and subtracting?
- The result keeps the least precise decimal place of the inputs. 7 is precise to the ones place and 0.063 to the thousandths, so 7 + 0.063 = 7.063 is reported to the ones place as 7.
- What is the sig fig rule for multiplying and dividing?
- The result keeps the fewest significant figures of the inputs. 2 has 1 sig fig and 2.35 has 3, so 2 × 2.35 = 4.7 is reported to 1 sig fig as 5.
- Why are the addition and multiplication rules different?
- Addition and subtraction are about absolute precision (decimal places), while multiplication and division are about relative precision (significant figures). A sum is only as precise as its coarsest term; a product is only as precise as its least-certain factor.
- Are trailing zeros significant?
- Only with a decimal point. 78800 has 3 significant figures because the trailing zeros are placeholders, but 78800. or 78800.0 makes them significant. Writing 2.00 instead of 2 declares three significant figures.
- Do exact numbers affect significant figures?
- No. Counted values and defined constants — 12 items in a dozen, 100 cm in a metre — have unlimited significant figures and never limit the result. Only measured quantities set the sig-fig count.
- Why does 2.00 × 2.35 give 4.70 but 2 × 2.35 gives 5?
- 2 has one significant figure, so the product rounds to one — 5. Writing 2.00 declares three significant figures, so the product keeps three and reports 4.70, trailing zero included.