Edexcel International GCSE Mathematics A · 4MA1
Upper and lower bounds
A rounded measurement stands for an interval of possible original values. Bounds describe the endpoints of that interval. For positive lengths, the smallest product uses the lower bounds and the largest product uses the upper bounds.
Key method
Take half the rounding unit below and above the reported value. For a positive quotient, its upper bound uses the largest numerator and smallest denominator.
Worked example
A rectangle is 8 cm by 5 cm, each rounded to the nearest centimetre. Find bounds for its area.
- The lengths satisfy 7.5 ≤ l < 8.5 and 4.5 ≤ w < 5.5.
- The lower area bound is 7.5 × 4.5 = 33.75.
- The upper area bound is 8.5 × 5.5 = 46.75.
Answer and interpretation
33.75 cm² ≤ A < 46.75 cm².
Common mistake
Applying a rounding interval directly to the area ignores uncertainty in both measured lengths.
Practise independently
A distance is 20 m to the nearest metre. State its error interval.
Check your answer
19.5 m ≤ d < 20.5 m.
Syllabus connection
This lesson develops upper and lower bounds within the number area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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