Approximation and Estimation
When an exam question wants a close value rather than an exact one: rounding with the error kept small, approximating percentages, fractions, squares and roots, breaking a product into round numbers, and using the answer options to decide how rough you can be.
What you will be able to do
- Round each term of an expression so the errors tend to cancel.
- Approximate a percentage-of or fraction-of quickly.
- Estimate a square, a square root and a large product.
- Use the spacing of the answer options to judge how rough an estimate can be.
What is inside this lesson
- 1What the question asks, and the error budget
- 2Round so the errors cancel
- 3Percentages and fractions
- 4Squares, roots and products
- 5Worked example: a messy expression
- 6Worked example: percentage of a number
- 7Worked example: a square root
- 8Common mistakes
- 9Quick revision
- 10Practice
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What the question asks, and the error budget
An approximation question ends with "...(approximate value)". You are not expected to compute the exact figure — only to get close enough to pick the right option, fast.
The options are usually spaced well apart — 240, 260, 280, 300 rather than 271, 272, 273. That spacing is your error budget. Glance at it before computing:
- Options 3 per cent or more apart: round freely to the nearest 10 or a clean fraction.
- Options within 1 to 2 per cent: round more carefully, and keep a running note of whether your estimate is above or below the true value.
- Two options survive: compute only the borderline term more exactly to break the tie, rather than redoing the whole line.
Never compute the exact answer to an approximation question — it wastes the time the question is designed to save.
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