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When a quantity is rounded, its true value lies within upper and lower bounds. This topic finds these bounds and uses them in calculations to give the range a rounded result could take. It's a core topic in GCSE and iGCSE Maths with Edexcel and the other major boards. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Find the bounds of each measurement first. For the largest possible answer, use the largest values when adding or multiplying, but the largest top and smallest bottom when dividing. For the smallest, do the reverse. Never round until the end.
Before you start
Everything here rests on error intervals and the four operations. It then feeds into accuracy in measurement and compound measures.
What you learn
When measurements are rounded, calculations with them have a range too. Bounds let you find the largest and smallest possible results — and division and subtraction need special care. The upper bound (UB) and lower bound (LB) are the largest and smallest values that round to the given measurement — half a unit each side. Subtraction and division swap one of the bounds — this is where marks are won or lost. The course works through finding bounds, bounds in sums and products and subtraction and division bounds. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Upper & Lower Bounds as one of the Number topics in our GCSE course library, at Higher tier. It runs to 3 concepts, each followed by a check, with 2 worked examples along the way. Students often pair it with Approximation, Compound Growth & Decay, Compound Interest & Decay, Error Intervals and FDP Equivalence. Endless extra practice on this strand is available on the Number revision engine, which generates a fresh question each time.
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