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Upper & Lower Bounds (H)

Tackle upper and lower bounds in GCSE Higher: interpret rounded data, find error intervals, and use bounds to estimate totals, speeds and areas.

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Fascinating Fact:

In ruler measurements, length 12.4 cm to 1 d.p. means lower bound = 12.35 cm and upper bound = 12.45 cm because the rounding step is 0.1 so half-step is 0.05.

In GCSE Maths (Higher), bounds show the range a rounded value could be. You’ll interpret rounding, write error intervals, and use upper/lower bounds to estimate results and justify accuracy.

Key Terms

Lower bound: The smallest value a rounded measurement could be; the start of its error interval.
Upper bound: The largest value a rounded measurement could be; the end of its error interval (typically not included).
Error interval: The range of possible values, often written as a ≤ value < b.

Frequently Asked Questions (Click to see answers)

What do upper and lower bounds mean in GCSE maths?

They are the greatest and least possible values of a rounded number. Together, they form an interval describing all values the original measurement could have been.

How do I find bounds from a rounded measurement?

Take half of the rounding unit. For 12.4 cm (1 d.p., unit 0.1), half is 0.05. So 12.35 ≤ length < 12.45. Lower = 12.35, upper = 12.45 (not included).

How are bounds used in calculations?

Use extreme cases to find possible results. For products/quotients, combine appropriate upper/lower bounds to estimate maximum or minimum values and report a sensible accuracy.