Estimation (Copy)
IGCSE CORE Mathematics Cheat Sheet: Rounding, Estimation & Degrees of Accuracy
1. Rounding Values to a Specified Degree of Accuracy
a) Rounding to Nearest 10, 100, 1000, etc.
- Look at the digit after the place you’re rounding to:
- If it’s 5 or more, round up.
- If it’s 4 or less, round down.
Examples:
- 5764 to nearest 1000 = 6000
- 5764 to nearest 100 = 5800
- 5764 to nearest 10 = 5760
b) Rounding to Decimal Places (d.p.)
- Count digits after the decimal point.
- Look at the next digit to decide whether to round up or down.
Example:
3.7869 to 2 d.p. = 3.79
c) Rounding to Significant Figures (s.f.)
- Start counting from the first non-zero digit.
- Round to the number of significant figures required.
Examples:
- 0.005678 to 2 s.f. = 0.0057
- 45678 to 2 s.f. = 46000
2. Estimation
- Estimation simplifies calculations by rounding numbers (usually to 1 significant figure) before calculating.
- Use estimation to check if answers are reasonable.
Example:
Estimate:
(9.79 × 0.765) ÷ 41.3
Round to 1 s.f.:
(10 × 0.8) ÷ 40 = 8 ÷ 40 = 0.2
3. Rounding Answers in Context
- Round final answers according to:
- The units involved (e.g., money → 2 d.p.).
- The precision of values given in the question.
Example:
If a length is calculated as 5.786 m and measurements were given to 1 decimal place, round to 1 d.p. → 5.8 m
4. Examples
- Nearest 10, 100, 1000:
1456 to nearest 100 = 1500 - Decimal Places:
12.3487 to 3 d.p. = 12.349 - Significant Figures:
0.009876 to 2 s.f. = 0.0099 - Estimate:
482 × 19 ≈ 500 × 20 = 10,000 - Estimate:
(298 ÷ 51) ≈ 300 ÷ 50 = 6
5. Quick Reference Rules
| Type | How to Round |
|---|---|
| Nearest 10/100/1000 | Look at next digit |
| Decimal Places (d.p.) | Count digits after decimal point |
| Significant Figures | Count from first non-zero digit |
| Estimation | Round each number to 1 s.f. before calculating |
6. Common Mistakes to Avoid
- Don’t confuse decimal places with significant figures.
- Always round final answers, unless asked to round within steps.
- For estimation, aim for simple numbers like multiples of 10 or 100.
- In word problems, match your rounding to the context (e.g., distances, money).
7. Tips for Exams
- Read carefully whether the question asks for d.p. or s.f..
- If no rounding instruction is given, round to 3 s.f. or match the input data’s accuracy.
- For money, always give answers to 2 decimal places.
- Use estimation to verify if calculator answers make sense.