What is important to know about Bounds & accuracy?

If a value is rounded to the nearest unit, the bounds are ± half a unit.

Lower bound = stated value − half the unit of rounding.

Upper bound = stated value + half the unit of rounding (but the upper bound itself is never reached).

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Number · Foundation & Higher

Bounds & accuracy

When a measurement is given to a certain degree of accuracy, the true value lies within an upper and lower bound.

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1If a value is rounded to the nearest unit, the bounds are ± half a unit.
2Lower bound = stated value − half the unit of rounding.
3Upper bound = stated value + half the unit of rounding (but the upper bound itself is never reached).
4For maximum of a sum: add upper bounds. For minimum of a sum: add lower bounds.
5For maximum of a quotient A÷B: use max A and min B.

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Lower bound

Rounded value − (rounding unit ÷ 2)

Upper bound

Rounded value + (rounding unit ÷ 2)

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Example 1

A length is measured as 8.4 cm to 1 d.p. Write down the upper and lower bounds.

Working

AnswerLB = 8.35 cm, UB = 8.45 cm

⚠️

✗Halving the last significant figure incorrectly.

✗Mixing up which operation needs upper/lower bounds (e.g. for division, max = max ÷ min).

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✓Write "LB =" and "UB =" clearly — examiners must see both.

✓For multi-step calculations with bounds, think about what combination gives the max or min result.

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