This sig fig calculator does the two things chemistry and physics classes actually require: count how many significant figures a number has, and round a number to a chosen number of significant figures. It also explains which rule applied — the part most students actually get marked down on.
Significant figures encode how precisely a value was measured. Writing 2.50 g claims you measured to the hundredth of a gram; writing 2.5 g claims only tenths. That is why sig figs survive every calculation rule in science courses: they stop you from inventing precision your instruments never had.
The Five Rules for Counting Sig Figs
Every case reduces to these rules:
- Non-zero digits are always significant: 123 has 3
- Zeros between non-zero digits are significant: 1002 has 4
- Leading zeros are never significant: 0.00520 has 3 (the 5, 2, and trailing 0)
- Trailing zeros AFTER a decimal point are significant: 12.300 has 5
- Trailing zeros WITHOUT a decimal point are ambiguous and conventionally NOT significant: 1200 has 2
To make trailing zeros count in a whole number, use scientific notation: 1.200 × 10³ has unambiguously 4 sig figs. In scientific notation, every digit of the mantissa is significant — which is exactly why scientists prefer it.
Rounding to N Significant Figures
Find the Nth significant digit, then round based on the digit after it:
- 3.14159 to 3 sig figs → 3.14
- 0.0025349 to 3 sig figs → 0.00253
- 98,765 to 2 sig figs → 99,000 (better written 9.9 × 10⁴)
Note the last case: the trailing zeros in 99,000 are placeholders, not precision — which is why the scientific-notation form is preferred after rounding whole numbers.
Sig Figs in Calculations
Two rules govern how precision propagates:
- Multiplication and division: the result keeps as many SIG FIGS as the least precise input. 2.5 × 3.42 = 8.55 → 8.6 (2 sig figs, because 2.5 has 2)
- Addition and subtraction: the result keeps as many DECIMAL PLACES as the least precise input. 12.11 + 18.0 = 30.11 → 30.1 (one decimal place, because 18.0 has one)
Exact numbers — counted quantities (24 students) and defined conversions (exactly 12 inches per foot) — have unlimited sig figs and never limit a result. And in multi-step problems, round only at the end: rounding intermediate values compounds error.
Frequently Asked Questions
How many sig figs does 0.00520 have?
Three — the 5, the 2, and the final 0. The three leading zeros only locate the decimal point and are never significant, while the trailing zero after a decimal point is significant because it claims measured precision.
How many significant figures does 1200 have?
By convention, two — the 1 and the 2. Trailing zeros in a whole number without a decimal point are ambiguous placeholders. Writing 1200. (with a decimal point) makes it 4 sig figs, and 1.20 × 10³ makes it unambiguously 3.
Do leading zeros count as significant figures?
Never. In 0.0042, only the 4 and 2 are significant — the zeros just position the decimal point. You can see this in scientific notation: 0.0042 = 4.2 × 10⁻³, and the leading zeros disappear entirely.
How do I round 98765 to 2 significant figures?
Keep the first two significant digits (9 and 8) and look at the next digit (7) to round: 98,765 → 99,000. Since the trailing zeros are now just placeholders, the cleaner form is 9.9 × 10⁴, which shows exactly 2 sig figs.
Why do significant figures matter?
They communicate measurement precision honestly. If a scale reads to 0.1 g, reporting 2.5473 g invents precision that does not exist; reporting 2.5 g states exactly what you know. In multi-step calculations, sig fig rules keep the final answer from claiming more certainty than the weakest measurement supports.