Significant figures
Objective. Round numbers to a stated number of significant figures.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A significant figure is any digit in a number that carries real information about its size, starting from the first non-zero digit. To round to a given number of significant figures, find that digit, then look at the next digit to decide whether to round up or keep it the same, filling remaining places with zeros where needed. For example, 0.03847 rounded to 2 significant figures is 0.038, because the first two significant digits are 3 and 8, and the next digit (4) rounds down. Leading zeros before the first non-zero digit are never counted as significant, but zeros between or after significant digits can be. This skill lets scientists and engineers report measurements at a sensible level of precision.
Worked example
Round areas 52 384 m² and 0.006721 m² each to 2 significant figures.
- 1For 52 384, the first two significant digits are 5 and 2; the next digit is 3, so round down.
- 252 384 to 2 s.f. is 52 000.
- 3For 0.006721, the first two significant digits are 6 and 7; the next digit is 2, so round down.
- 40.006721 to 2 s.f. is 0.0067.
Answer: 52 000 m² and 0.0067 m²
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often count leading zeros as significant, rounding 0.00456 to 3 s.f. as 0.00500 instead of 0.00456 itself already being 3 s.f. Always locate the first non-zero digit before counting.
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