AS Level Physics · Physical quantities and units. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
No measurement is exact. A systematic error shifts every reading the same way by the same amount, for example a balance that reads 0.2 g with nothing on it (a zero error). Repeating readings does not remove it. You must correct the readings or the method. A random error scatters readings unpredictably above and below the true value. Repeating and taking the mean reduces its effect.
Accuracy is how close a result is to the true value. Precision is how close repeated readings are to each other. Readings can be precise but not accurate.
When you calculate a quantity from measured values, the uncertainties of those values combine to give the uncertainty in the result.
Subtracting the uncertainties when two quantities are subtracted or divided. Uncertainties always add, whatever the operation.
Answer: About 3.9% (4% to one significant figure).
Try each one, then open the answer.
Answer: C. For a quotient add percentage uncertainties: 0.2/6.0 = 3.3% and 0.1/2.0 = 5%, total 8.3%.
Answer: C. Area ∝ d2, so the percentage uncertainty doubles: 2 × (0.01/0.50) = 2 × 2% = 4%.
Answer: A. Precision is the closeness of repeated readings to each other; accuracy is closeness to the true value. Tightly grouped but offset readings are precise, not accurate.
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