Significant Figures Calculator
Count significant figures, round a value, or apply significant-figure rules to addition, subtraction, multiplication and division.
Significant-figure rules used
- All nonzero digits are significant.
- Zeros between nonzero digits are significant.
- Leading zeros are placeholders and are not significant.
- Trailing zeros after a decimal point are significant.
- Trailing zeros in a whole number without a decimal point are treated as ambiguous placeholders. Use scientific notation to state them explicitly.
- For multiplication and division, the result keeps the fewest significant figures among the inputs.
- For addition and subtraction, the result is rounded to the least precise decimal place among the inputs.
Checked examples
| Input or operation | Rule | Result |
|---|---|---|
| 0.004560 | Leading zeros do not count; trailing decimal zero counts | 4 significant figures |
| 1.20 × 10³ | Every digit in the coefficient counts | 3 significant figures |
| 12,345 rounded to 3 figures | Next digit is 4 | 12,300 (1.23 × 10⁴) |
| 9.99 rounded to 2 figures | Carry propagates | 10 (1.0 × 10¹) |
| 12.11 + 0.3 | Round to tenths | 12.4 |
| 4.56 × 1.4 | Fewest input count is 2 | 6.4 |
Counting versus rounding
Counting reads the precision communicated by the written number. For example, 2.50 has three significant figures, while 2.5 has two. Rounding changes a value to the requested precision. Scientific notation is shown with every rounded result so trailing zeros remain unambiguous.
Limits and interpretation
The calculator supports ordinary decimal and e-notation inputs within JavaScript’s finite numeric range. Counting and single-number rounding use the entered digit string, so written trailing zeros are preserved. Arithmetic uses floating-point computation before applying the selected precision rule; it is intended for general educational and engineering calculations, not arbitrary-precision financial accounting.
Frequently asked questions
Are trailing zeros significant?
They are significant when a decimal point makes the intended precision explicit, as in 12.00. In 1200 without a decimal point, the number of significant trailing zeros is ambiguous, so this calculator treats them as placeholders.
Does scientific notation change the number of significant figures?
No. Only the digits in the coefficient determine the count. The exponent changes the scale, not the precision.
Why do addition and multiplication use different rules?
Addition and subtraction are limited by decimal place. Multiplication and division are limited by the count of significant figures.