The significant figure rules
- Non-zero digits are always significant.
- Captive zeros between non-zero digits are significant: 4,508 has 4.
- Leading zeros are never significant: 0.0072 has 2.
- Trailing zeros after a decimal point are significant: 0.00720 has 3, and 2.0 has 2.
- Trailing zeros in a whole number without a decimal point are ambiguous: 1200 could have 2, 3 or 4. Most courses count 2. Write 1.20 × 10³ or “1200.” to be clear.
Exact numbers (counted items, defined conversions like 100 cm = 1 m) have unlimited significant figures and never limit a result.
Rules for calculations
Multiplying or dividing: the answer keeps as many sig figs as the input with the fewest. 12.52 × 3.1 = 38.812 → 39 (2 sig figs, because of 3.1).
Adding or subtracting: the answer is rounded to the least precise decimal place. 12.52 + 3.1 = 15.62 → 15.6 (tenths, because of 3.1).
In multi-step problems, keep extra digits along the way and round once at the end, otherwise rounding errors accumulate.
Frequently asked questions
How many sig figs does 100 have?
By the usual textbook convention, 1: the trailing zeros are ambiguous placeholders. 100. (with a decimal point) has 3, and 1.00 × 10² has 3.
Do zeros after a decimal count?
Trailing zeros after the decimal point do (2.50 has 3). Leading zeros before the first non-zero digit don’t (0.05 has 1).
How do I round 0.004050 to 2 sig figs?
The first two significant digits are 4 and 0; the next digit is 5, so round up: 0.0041.