Estimation and approximation checking

WJEC awards method marks for sensible estimates and for using approximation as a sanity check on a calculator answer.

Why estimate?

• To predict an answer's order of magnitude before calculating.
• To check a calculator result for plausibility.
• To answer "estimate" questions where exact arithmetic is unnecessary or impossible.

The 1-significant-figure method

Round each number in a calculation to 1 significant figure, then evaluate.

Example: estimate (38.7 × 4.93) / 2.08.

• 39 → 40, 4.93 → 5, 2.08 → 2.
• Estimate = (40 × 5) / 2 = 100.
• True value = 91.7… — the estimate is in the right ballpark.

Square roots

Estimate √78 by finding the nearest perfect squares: 64 (= 8²) and 81 (= 9²). So √78 is between 8 and 9, closer to 9. A reasonable estimate is 8.8.

Cube roots

Cube roots: 27 = 3³, 64 = 4³, 125 = 5³, 216 = 6³, 343 = 7³, 512 = 8³.

So ³√100 lies between 4 and 5; closer to 5 since 100 is closer to 125 than to 64. Reasonable estimate ≈ 4.6.

When to use estimation as a check

After any multi-step calculator answer, jot a 1-s.f. estimate in the margin. If your computed result is more than 50% off, you've likely keyed something incorrectly.

"Show that" estimation problems

WJEC sometimes asks: "Show that 47.8 × 0.198 ÷ 0.51 is approximately equal to 20."

• Round: 48 × 0.2 ÷ 0.5 = 9.6 / 0.5 = 19.2.
• Or: 50 × 0.2 ÷ 0.5 = 20.

Both are acceptable methods; the simpler the rounding, the better.

WJEC exam tip

When asked to ESTIMATE, write the rounded values explicitly on the page M1 before computing. Examiners credit the rounding method even if the arithmetic at the end has a small slip.