Rounding: significant figures and decimal places

Rounding is tested on every OCR J560 paper. A common source of lost marks is using the wrong number of significant figures. This topic also underpins bounds (N16) and estimation (N14).

Decimal places (d.p.)

Decimal places count digits after the decimal point.

• Round to 1 d.p.: look at the 2nd decimal place. If ≥ 5, round up; if < 5, round down.
• Example: 3.472 to 1 d.p. → look at 7 (2nd decimal) → ≥ 5 → 3.5.
• Example: 7.843 to 2 d.p. → look at 3 (3rd decimal) → < 5 → 7.84.

Significant figures (s.f.)

Significant figures count from the first non-zero digit.

Rules:

1. Start counting from the first non-zero digit.
2. Zeros BETWEEN significant figures ARE significant: 4052 has 4 s.f.
3. Trailing zeros AFTER the decimal point ARE significant: 3.80 has 3 s.f.
4. Leading zeros (before the first non-zero digit) are NOT significant: 0.0047 → first s.f. is 4.

Examples:

• 47,832 to 3 s.f. → 47,800 (look at the 4th digit: 3, so round down; fill with zeros to maintain place value).
• 0.004672 to 2 s.f. → 0.0047 (first two s.f. are 4 and 6; look at 7, round up).
• 9.985 to 3 s.f. → 9.99 (the 4th digit is 5, round up → 9.985 → 9.99, NOT 10.0 — keep 3 s.f.).

Careful with carry: 3.995 to 3 s.f. → 4th digit is 5 → round up → 4.00 (still 3 s.f., note the trailing zeros are significant here).

Rounding in context

"Give your answer to an appropriate degree of accuracy" — for most measurement contexts at GCSE, 3 s.f. is appropriate unless otherwise stated. For money: 2 d.p.

Estimation

Round each value to 1 s.f. to get a quick approximation.

Example: Estimate 387 × 52 ÷ 19 ≈ 400 × 50 ÷ 20 = 20,000 ÷ 20 = 1,000.

Common OCR exam mistakes

1. Counting leading zeros as significant figures: 0.0047 has 2 s.f. not 4.
2. Not filling with zeros when rounding large numbers: 47,832 to 3 s.f. should be 47,800 NOT 478.
3. Stopping the rounding before carrying: 9.985 to 3 s.f. needs to carry through to 9.99, not stop at 9.98.
4. Rounding too early in multi-step calculations — only round the final answer unless the question explicitly asks you to round at an intermediate step.