Advanced estimation
Objective. Estimate complex calculations using suitable approximations.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Advanced estimation means approximating each number in a complex calculation to one significant figure before combining them, so a quick, sensible answer can be checked against a calculator result. The method is to round every value, perform the arithmetic with the simplified numbers, and present the estimate clearly rather than an exact figure. For example, to estimate (48.7 × 9.3) ÷ 2.1, round to 50 × 9 ÷ 2, giving 450 ÷ 2 = 225. This approach is especially useful for calculations mixing multiplication, division and roots, where rounding first makes mental arithmetic manageable. Estimation also helps spot calculator entry mistakes, since a wildly different exact answer signals an error.
Worked example
Use estimation to approximate the value of (203 × 4.8) ÷ 9.7.
- 1Round each number to 1 significant figure: 203 ≈ 200, 4.8 ≈ 5, 9.7 ≈ 10.
- 2Substitute: (200 × 5) ÷ 10.
- 3Numerator: 200 × 5 = 1000.
- 41000 ÷ 10 = 100.
Answer: 100
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes round only one number in the calculation and leave the rest exact, producing an estimate that is not genuinely simplified. Round every value to 1 significant figure before calculating.
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