Significant Figures Calculator
Round a number to any number of significant figures and identify sig figs.
The Rules for Significant Figures
Significant figures communicate the precision of a measurement — they indicate which digits are actually meaningful based on the measuring instrument's capabilities. The rules: all nonzero digits (1–9) are always significant. Zeros between nonzero digits are significant (4,002 has 4 sig figs). Leading zeros (placeholders before the first nonzero digit) are never significant (0.0045 has 2 sig figs). Trailing zeros after a decimal point are significant (3.50 has 3 sig figs, indicating measurement to the hundredths). Trailing zeros in a whole number without a decimal point are ambiguous (1200 could be 2, 3, or 4 sig figs).
Sig Figs in Calculations
When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest sig figs. When adding or subtracting, the result should have the same number of decimal places as the measurement with the fewest decimal places. These rules prevent a calculation from falsely implying more precision than the least precise input justifies — if you measure with a ruler accurate to 1mm, your area calculation should not be reported to 6 decimal places.
Scientific Notation Eliminates Ambiguity
The ambiguity of trailing zeros in whole numbers is resolved by scientific notation. 1200 with 3 sig figs becomes 1.20 × 10³. 1200 with 2 sig figs becomes 1.2 × 10³. In scientific work, results are always reported in scientific notation or with explicit decimal points to remove any doubt about the intended precision.
Frequently Asked Questions
Why do significant figures matter?
Sig figs communicate the precision of a measurement. Reporting 12.345 when your instrument only measures to 0.1 implies false precision. Scientists use sig figs to accurately convey measurement uncertainty.
How many sig figs does 100 have?
Ambiguous u2014 it could be 1, 2, or 3. To be unambiguous, write 1.0 u00d7 10u00b2 (2 sig figs) or 1.00 u00d7 10u00b2 (3 sig figs) using scientific notation.