Significant Figures Calculator
Count the significant figures in a number, classify every digit (leading, captive or trailing zero), round to a chosen number of sig figs with half-to-even rounding, or apply the sig-fig rules to addition, subtraction, multiplication and division.
Written by Suhaib Hassan. Every rule below follows the standard significant-figures convention taught in introductory science courses. Our methodology.
Digits are classified by position relative to the decimal point; rounding uses exact half-to-even arithmetic on the digit string, not floating-point rounding, so results match textbook rules precisely.
Trailing zeros are the most commonly misjudged case — this shows exactly why each digit does or doesn't count.
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Digit-by-digit classification
Which digits count as significant, and why.
Step-by-step working
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The significant-figures rules
Which zeros count.
| Digit type | Example | Significant? |
|---|---|---|
| Non-zero digits | 1–9 anywhere | Always significant |
| Captive zeros | 1005 | Always significant |
| Leading zeros | 00405 | Never significant |
| Trailing zeros, with a decimal point | 4.500 | Significant |
| Trailing zeros, no decimal point | 12000 | Ambiguous — write in scientific notation to clarify |
Worked examples
Trailing zeros with a decimal
How many sig figs does 0.0040500 have?
5 significant figures
Addition rule
Add 12.11 and 18.0.
round to fewest decimal places (1)
30.1
Multiplication rule
Multiply 4.5 by 2.10.
round to 2 s.f.: the dropped digit is exactly 5 with nothing after, and the kept digit 4 is already even
9.4 (half-to-even keeps the tie at the even digit)
Why significant figures matter
Significant figures record how precisely a quantity was measured. Writing 4.50 cm instead of 4.5 cm claims an extra digit of real precision; a calculated result can never be more precise than the least precise measurement that went into it, so results must be rounded to match.
The two arithmetic rules
- Addition & subtraction: round the result to the same number of decimal places as the operand with the fewest decimal places.
- Multiplication & division: round the result to the same number of significant figures as the operand with the fewest significant figures.
- Rounding ties: when the digit being dropped is exactly 5 with nothing after it, round to the nearest even digit (half-to-even / banker's rounding), which avoids a systematic upward bias.
By Suhaib Hassan · Reviewed 29 September 2026 · How CalculatePilot verifies formulas →
Sources
- Taylor, J. R. (1997). An Introduction to Error Analysis (2nd ed.). University Science Books, chapter 2.
- NIST Special Publication 811 (2008). Guide for the Use of the International System of Units (SI), section 7.
- ISO 80000-1:2022, Quantities and units — Part 1: General.
Frequently asked questions
Does 100 have 1, 2 or 3 significant figures?
It is ambiguous as written — by the common convention this calculator uses, trailing zeros with no decimal point are not significant, so "100" reads as 1 sig fig. Writing 100. (with a trailing decimal point) or 1.00 × 10² removes the ambiguity and gives 3 sig figs.
Are exact numbers and defined constants exempt?
Yes. Counting numbers (12 eggs) and exactly defined conversion factors (100 cm = 1 m, by definition) have effectively infinite significant figures and never limit the precision of a calculation.
Why does half-to-even rounding exist?
Always rounding a trailing 5 up introduces a small systematic bias over many roundings. Rounding to the nearest even digit instead splits ties evenly between rounding up and down, keeping large-sample averages unbiased.
How are significant figures different from decimal places?
Decimal places count digits after the decimal point regardless of where they start; significant figures count meaningful digits starting from the first non-zero digit. 0.002 has 3 decimal places but only 1 significant figure.
What about scientific notation?
Scientific notation removes all ambiguity: every digit in the mantissa (the part before ×10ⁿ) is significant by convention, since no digit is needed purely to place the decimal point.
Does the sig-fig rule apply the same way to subtraction as addition?
Yes — subtraction follows the same decimal-places rule as addition. Note that subtracting two close, imprecise numbers can dramatically reduce the number of significant figures in the result (called "catastrophic cancellation").
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