Significant figures in simple words
Significant figures (sig figs) are the digits in a number that carry real meaning about how carefully it was measured.
The rules: digits 1 to 9 always count. Zeros between other digits count, like the 0 in 105. Zeros at the start never count, like in 0.004. Zeros at the end count only when there is a decimal point, like in 2.50.
For example, 0.004560 has 4 significant figures: 4, 5, 6 and the last 0. The zeros at the front only show where the decimal point is.
To round to 3 significant figures, keep the first 3 meaningful digits (4, 5, 6) and look at the next one. It is 0, so nothing rounds up: the answer is 0.00456.
Formula and method
Start at the first nonzero digit, retain the requested count and round the discarded part. Scientific notation makes retained trailing zeros unambiguous.
Worked example
9.999 rounded to three significant figures is 1.00 × 10¹. The carry changes the exponent while the three retained digits remain explicit.
Counting significant figures
Nonzero digits are always significant. Zeros between nonzero digits are significant (1002 has four). Leading zeros only place the decimal point (0.0045 has two). Trailing zeros are significant when a decimal point is written (4.50 and 1200. have three and four).
Trailing zeros in a whole number with no decimal point are ambiguous: 1200 could have two, three or four significant figures. The counter shows the range; write 1.20 × 10³ or 1200. to make your precision explicit.
Calculating with measurements
For addition and subtraction, round the result to the least precise decimal place among the inputs: 12.11 + 18.0 = 30.11, which rounds to 30.1 because 18.0 ends in the tenths place.
For multiplication and division, keep the fewest significant figures among the inputs: 2.5 × 3.42 = 8.55, which rounds to 8.6 because 2.5 has two significant figures. Round only the final answer, not intermediate results.