Significant Figures Calculator
Count sig figs, round to any number of them, and apply the multiplication and addition rules
How many significant figures?
A decimal point is written, so trailing zeros ARE significant.
Counted digits: 1 2 0 0 0
Apply the rules to a calculation
Multiplication and division: the result keeps the FEWEST significant figures of the inputs.
Limited to 2 significant figures.
The rules, in the order they apply
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits always count | 45.6 | 3 |
| Zeros between non-zero digits count | 1002 | 4 |
| Leading zeros never count | 0.00452 | 3 |
| Trailing zeros with no decimal point are ambiguous | 1200 | 2 |
| …but count when a decimal point is written | 1200. | 4 |
| Trailing zeros after the point always count | 0.1200 | 4 |
| Only the mantissa counts in scientific notation | 1.20×10³ | 3 |
| Exact / counted numbers are unlimited | 12 eggs | ∞ |
The two arithmetic rules are not the same rule
This is where most marks are lost. Multiplication and division are limited by the fewest significant figures; addition and subtraction are limited by the fewest decimal places.
- 2.5 × 3.42 = 8.55 → 2.5 has 2 sig figs, so the answer is 8.6.
- 100.0 + 0.001 = 100.001 → the fewest decimal places is one, so the answer is 100.0. Applying the sig-fig rule here would give “1 × 10²”, which is wrong — 0.001 has one significant figure but it does not destroy the precision of 100.0.
Why 1200 is not four significant figures
Significant figures record how precisely something was measured. Written bare, 1200 could be a value measured to the nearest hundred or to the nearest unit, and the notation cannot tell you which — so the convention is to count only the two digits you can be sure about. Writing 1200. or 1.200×10³ removes the ambiguity, which is the main practical reason scientific notation exists.
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Frequently Asked Questions
What are the rules for significant figures?
Non-zero digits always count. Zeros between non-zero digits always count (1002 has 4). Leading zeros never count (0.00452 has 3). Trailing zeros count only when a decimal point is written — 1200 has 2, but 1200. has 4 and 1200.0 has 5. In scientific notation only the mantissa counts, so 1.20×10³ has 3.
How many significant figures does 1200 have?
Two. Without a written decimal point the trailing zeros are ambiguous and are not counted. If you mean all four to be significant, write 1200. or 1.200×10³ — that is exactly what scientific notation is for.
Are the rules different for adding and multiplying?
Yes, and this is the most common mistake. Multiplication and division keep the fewest SIGNIFICANT FIGURES of the inputs. Addition and subtraction keep the fewest DECIMAL PLACES. So 100.0 + 0.001 = 100.0, even though 0.001 has only one significant figure.
Do leading zeros ever count?
No. They only place the decimal point, they carry no measurement precision. 0.00452, 0.0452 and 0.452 all have three significant figures.
What about exact numbers, like 12 in a dozen?
Counted or defined numbers are exact and have infinite significant figures, so they never limit the precision of a result. If you divide a measured mass by exactly 3 samples, the 3 does not restrict your answer to one significant figure.
How do I round to significant figures?
Keep the required number of significant digits, then look at the next digit: 5 or more rounds up, less rounds down. Fill the remaining places with zeros to keep the magnitude. 45,678 to 2 significant figures is 46,000; 0.0045678 to 3 is 0.00457.