Significant figures (s.f.) indicate the precision of a measurement or calculation. Using too many or too few can lose marks.
Rules for counting significant figures
- All non-zero digits are significant: 345 has 3 s.f.
- Zeros between non-zero digits are significant: 3045 has 4 s.f.
- Leading zeros are not significant: 0.0032 has 2 s.f.
- Trailing zeros after a decimal point are significant: 3.20 has 3 s.f.
- Trailing zeros in a whole number without a decimal point are ambiguous: 300 could be 1, 2 or 3 s.f.
Standard form removes ambiguity
Writing 300 as 3.00 x 10^2 makes it clear the value has 3 s.f. Writing it as 3 x 10^2 shows 1 s.f.
How many significant figures to give
General rule: give your answer to the same number of significant figures as the least precise value in the data. If the question does not specify, use 2 or 3 s.f.
Example: A force of 25 N acts over a distance of 3.0 m. Work = 25 x 3.0 = 75 J. Both values have 2 s.f., so the answer is 75 J (2 s.f.).
Do not round intermediate steps
If a calculation has multiple steps, keep extra digits in intermediate results. Only round the final answer.
Common mistake
Giving a calculator answer of 7.142857142857… to 10 decimal places. The examiner expects 7.1 (2 s.f.) or 7.14 (3 s.f.), depending on the data.
When precision matters in measurements
If a ruler measures to the nearest mm, a reading of 23.0 cm has 3 s.f. Recording it as 23 cm suggests you only measured to the nearest cm, which misrepresents the precision of your instrument.
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