Error intervals in context
Objective. Write and interpret error intervals for measurements rounded to different degrees of accuracy.
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- 2. Worked example
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Learn: the key idea
An error interval states the range of possible exact values a measurement could take before it was rounded. If a length is given as 7 cm to the nearest cm, the true value lies between 6.5 cm (inclusive) and 7.5 cm (exclusive), written 6.5 ≤ l < 7.5. The lower bound is half the rounding unit below the stated value, and the upper bound is half the rounding unit above it. The upper bound always uses a strict inequality because rounding up to the next value would change the stated rounded figure. Always match the half-unit to the degree of accuracy given, whether whole numbers, 1 decimal place, or significant figures.
Worked example
A mass is recorded as 420 g to the nearest 10 g. Write the error interval for the true mass m.
- 1Rounding unit is 10 g, so half the unit is 5 g.
- 2Lower bound = 420 − 5 = 415 g.
- 3Upper bound = 420 + 5 = 425 g, but this value itself would round up, so use a strict inequality.
- 4Error interval: 415 ≤ m < 425.
Answer: 415 ≤ m < 425
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Start practisingCommon mistake. Pupils often write the upper bound with ≤ instead of <, e.g. 6.5 ≤ l ≤ 7.5 for a value rounded to the nearest cm. Remember 7.5 itself would round to 8, so the upper bound must be strict.
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