Quick revision notes · Mathematics 4024 · Chapter 4 of 35
Significant Figures
Decimal places, significant figures, estimating, and how accurate an answer should be.
4 sectionsWorked examples
Common mistakes
At a glance
Decimal places, significant figures, estimating, and how accurate an answer should be.
1Rounding to decimal places
- Count the places after the decimal point, then look at the next digit.
- 5 or more → round up; 4 or less → leave the digit.
- Keep the trailing zero if the question asks for it: 2.497 to 2 d.p. is 2.50, not 2.5.
Worked example
Round 3.14159 to 2 decimal places.
- Two places: 3.14|159.
- The next digit is 1 → stays.
3.14
2Rounding to significant figures
- The first significant figure is the first non-zero digit.
- Zeros at the start of a decimal never count: 0.004682 → first s.f. is 4.
- Zeros between non-zero digits do count: 3005 has 4 s.f.
- Keep the size of the number with place-value zeros: 68 451 to 3 s.f. = 68 500.
| Number | 1 s.f. | 2 s.f. | 3 s.f. |
|---|---|---|---|
| 68 451 | 70 000 | 68 000 | 68 500 |
| 0.004682 | 0.005 | 0.0047 | 0.00468 |
| 2.0496 | 2 | 2.0 | 2.05 |
Worked example
Round 0.004682 to 2 significant figures.
- First s.f. is the 4; two s.f. = 0.0046|82.
- Next digit 8 → round up.
0.0047
3Estimating a calculation
- Round every number to 1 significant figure, then work it out without a calculator.
- Show the rounded numbers — the method mark is for them.
- Dividing by a decimal: 200 ÷ 0.2 = 2000 ÷ 2 = 1000.
- Overestimate or underestimate? If you rounded the numbers you multiply up, the estimate is too big.
How to do it
- Round each number to 1 s.f.
- Write the new calculation down.
- Work it out (simplify fractions first).
Worked example
Estimate (38.7 × 5.12) ÷ 0.198.
- Round: 40 × 5 ÷ 0.2.
- 40 × 5 = 200.
- 200 ÷ 0.2 = 1000.
1000
Exam tip: A square root estimate: round to the nearest square number, e.g. √48.6 ≈ √49 = 7.
4Choosing a sensible accuracy
- Unless the question says otherwise, give answers to 3 significant figures (or exact).
- Angles in degrees: 1 decimal place. Money: to the nearest cent.
- Never round in the middle of a calculation — keep the full calculator value and round only the final answer.
- If the answer is exact (like 7.25), write it in full rather than rounding it.
Worked example
A rectangle is 3.47 m by 2.6 m. Find its area to a sensible accuracy.
- 3.47 × 2.6 = 9.022.
- Round to 3 s.f.
9.02 m²
✗Common mistakes
| Don’t write | Write instead |
|---|---|
| 68 451 to 3 s.f. = 685 | Keep the place-value zeros: 68 500 |
| 0.004682 to 2 s.f. = 0.00 | Start counting at the first non-zero digit: 0.0047 |
| Rounding halfway through a calculation | Keep full values; round at the end |
| Estimating with the exact numbers | Round each number to 1 s.f. first and show it |
★In the exam
- Write the full calculator answer down before you round it — it can earn a mark if your rounding slips.
- If the question says 'to 2 d.p.' give exactly 2 decimal places, including a final zero.
- An answer to 3 s.f. is the Cambridge default: 2.71828 → 2.72.