Significant figures, explained with simple rules

Significant figures are the digits in a number that mean something. They tell the reader how precisely a quantity was measured. A ruler marked in millimetres can give 12.4 cm. Writing 12.4000 cm would pretend you measured to the nearest hundredth of a millimetre, and nobody believes that.

Counting them

• Non-zero digits always count. 4,583 has four.
• Zeros between non-zero digits count. 10,042 has five.
• Leading zeros never count. 0.0035 has two, because the zeros only show where the decimal point is.
• Trailing zeros after a decimal point count. 2.50 has three: the zero says you measured to that place.
• Trailing zeros in a whole number are ambiguous. Does 1,500 have two, three or four? Scientific notation settles it: 1.5 × 10³ has two, 1.50 × 10³ has three.

Rounding to a set number of figures

Find the digit in the last place you want to keep, look at the digit after it, and round up if it is 5 or more. Rounding 0.0047382 to three significant figures: the first significant digit is 4, so we keep 4, 7 and 3. The next digit is 8, so the 3 goes up. The answer is 0.00474.

Which rule applies in a calculation?

Operation	Rule	Example
Multiply or divide	Keep as many significant figures as the least precise input	2.5 × 3.14 = 7.9 (two figures)
Add or subtract	Keep as many decimal places as the least precise input	12.1 + 0.256 = 12.4

Do not round in the middle

Keep a couple of extra digits in intermediate steps and round only at the end. Rounding at every line piles up small errors, and your final answer can drift a unit in the last place.

A worked example

A pupil measures a rectangle as 4.2 cm by 3.75 cm. The product on a calculator is 15.75. The width 4.2 has two significant figures, so the area is quoted as 16 cm². It looks like throwing information away, but it is an honest statement of how well the sides were measured.