The number of significant figures in your final answer should match the precision of your data
Measurements & Uncertainties - OCR A-Level Physics
Key Definition
Significant figures (s.f.)
The digits in a measurement that carry real information about its value. Leading zeros do not count; trailing zeros after a decimal point do. The number of significant figures in a final answer is set by the least precise measurement used in the calculation.
The digits in a measurement that carry real information about its value. Leading zeros do not count; trailing zeros after a decimal point do. The number of significant figures in a final answer is set by the least precise measurement used in the calculation.
- The final answer should be given to the same number of significant figures as the data in the question, usually 2 or 3 s.f.
- Your result cannot be more precise than the least precise measurement used to calculate it. If a length is 0.45 m (2 s.f.), the answer is 2 s.f. as well.
- The uncertaintyThe range of confidence in a measurement, written as ± a value giving the upper and lower bounds within which the true value is expected to lie. tells you which digits are meaningful. An answer of $9.81 \pm 0.05 \text{ m s}^{-2}$ has only three meaningful digits, so reporting 9.8134 makes no sense.
- The rule for rounding: round the uncertainty to 1 s.f. first, then round the result so its last digit lines up with the uncertainty.
- OCR mark schemes accept an answer one s.f. either side of the expected value. Outside that range you lose the mark.
$$3.456 \pm 0.073 \rightarrow 3.46 \pm 0.07$$
Common Mistake
MEDIUM
Wrong: Copying every digit from the calculator into the answer box. A reading of 0.45 m used to calculate density gives an answer like $1234.5678 \text{ kg m}^{-3}$.
Right: Round to the lowest number of s.f. in your data. With one input at 2 s.f., the final answer is also 2 s.f., so $1200 \text{ kg m}^{-3}$ or $1.2 \times 10^{3} \text{ kg m}^{-3}$.
Right: Round to the lowest number of s.f. in your data. With one input at 2 s.f., the final answer is also 2 s.f., so $1200 \text{ kg m}^{-3}$ or $1.2 \times 10^{3} \text{ kg m}^{-3}$.
Examiner Tips and Tricks
- In practical papers and Section B calculations, you will lose a mark for giving too many or too few significant figures.
- Keep extra digits during intermediate working, then round only at the very end.
- If you are unsure, match the s.f. of the data in the question stem.