Rounding to an appropriate degree of accuracy
WJEC tests rounding both as a stand-alone skill and as the final step of a multi-stage calculation.
Decimal places (d.p.)
Look at the digit AFTER the cut-off:
- 0–4 → round down (digit unchanged).
- 5–9 → round up (digit + 1).
Example: 3.4628 to 2 d.p. → look at the 3rd decimal (2) → round down → 3.46.
Significant figures (s.f.)
The first significant figure is the first non-zero digit. Count from there.
Example: 0.004572 to 2 s.f. → first s.f. is 4; second is 5; next digit is 7 → round up → 0.0046.
Example: 53 271 to 2 s.f. → first is 5; second is 3; next is 2 → round down → 53 000.
Trailing zeros after rounding ARE significant in context but are kept to mark the magnitude.
Choice of accuracy
The "appropriate" accuracy depends on context:
- Money to the nearest penny → 2 d.p.
- Lengths in metres for everyday use → 2 or 3 s.f.
- Population → nearest 1000 or 100 000 depending on size.
- Temperature → 1 d.p. for medical use.
Don't round mid-calculation
Carrying a rounded value through several steps compounds error. Keep full calculator precision until the LAST step, then round.
Truncation vs rounding
WJEC does not normally examine truncation, but mention it: truncation chops the trailing digits without checking. 3.49 truncated to 1 d.p. is 3.4 (NOT 3.5). Always check the question says "round" — if so, use standard rounding rules.
✦Worked example
Calculate (12.46 + 3.812) × 4.93 to 3 s.f.
Full precision: 16.272 × 4.93 = 80.22096... Round to 3 s.f.: 80.2.
DON'T round 16.272 → 16.3 first; that gives 80.359, rounded to 80.4 — a different (and wrong) answer.
WJEC exam tip
When the question says "give your answer to a reasonable degree of accuracy", 3 s.f. is almost always safe. Avoid more than 3 s.f. unless the input data is more precise; avoid 1 s.f. unless explicitly asked.
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