Estimation
O Level and IGCSE Mathematics Cheat Sheet – 1.9 Estimation
Rounding – Key Types
| Type | Rule | Example |
|---|---|---|
| Nearest 10, 100, 1000, … | Look at digit to the right; ≥5 round up, <5 round down | 5764 → nearest 1000 = 6000 |
| Decimal Places (d.p.) | Keep required digits after decimal point | 3.746 → 2 d.p. = 3.75 |
| Significant Figures (s.f.) | First non-zero digit is 1st s.f., round to required s.f. | 0.004563 → 2 s.f. = 0.0046 |
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Estimation in Calculations
- Round each number to 1 significant figure.
- Do calculation mentally or simply.
- Answer is approximate.
Example: Estimate (9.79 × 0.765) ÷ 41.3
- Round: 9.79 ≈ 10, 0.765 ≈ 0.8, 41.3 ≈ 40
- Estimate: (10 × 0.8) ÷ 40 = 8 ÷ 40 = 0.2
When to Round
- During working for estimation problems — round before calculation.
- At the end for final answers in normal problems — use context to decide accuracy.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Choosing a Reasonable Degree of Accuracy
- Measurements → match given accuracy of data.
- Money → 2 decimal places (cents/paisa).
- Counts → nearest whole number.
Decimal Places vs Significant Figures
| Example Number | 2 d.p. | 2 s.f. |
|---|---|---|
| 3.746 | 3.75 | 3.7 |
| 0.004563 | 0.00 | 0.0046 |
Exam Special Tips
- For estimation, don’t over-round — use 1 s.f. unless problem says otherwise.
- In word problems, final answer accuracy should match the least accurate data given.
- Watch for rounding twice — this can cause large errors.
- Show your rounded values in working to get method marks.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Common Mistakes & Confusions
- Confusing decimal places with significant figures.
- Rounding too early in non-estimation problems, causing inaccuracy.
- Forgetting that 0 can be significant if it’s between non-zero digits or after a decimal.