ZIMSEC O Level · Mathematics · Form 1, Form 2
In real measurements we round numbers. Exam questions ask for a given number of decimal places or significant figures.
Decimal places and significant figures
- Decimal places (d.p.) are counted after the decimal point: 3.14159 = 3.14 (2 d.p.).
- Significant figures (s.f.) are counted from the first non-zero digit: 0.004567 = 0.00457 (3 s.f.); 48 650 = 48 700 (3 s.f.).
- Look at the next digit: 5 or more rounds up; 4 or less rounds down.
Standard form
A number in standard form is written A × 10ⁿ where 1 ≤ A < 10 and n is an integer.
- Large numbers: 45 000 000 = 4.5 × 10⁷
- Small numbers: 0.00072 = 7.2 × 10⁻⁴
Worked example: Calculate (3 × 10⁵) × (6 × 10³), giving the answer in standard form.
3 × 6 = 18 and 10⁵ × 10³ = 10⁸
18 × 10⁸ = 1.8 × 10⁹
Estimation
Round each number to 1 significant figure to check that a calculator answer is sensible.
Worked example: Estimate 48.7 × 0.312 ÷ 9.8.
≈ 50 × 0.3 ÷ 10 = 1.5
Exam tip: Always check that A is between 1 and 10. 18 × 10⁸ is NOT in standard form.
Check yourself
- Round 0.0060493 to 3 significant figures.
- Write 0.000 305 in standard form.
- Calculate (8.4 × 10⁶) ÷ (2.1 × 10²).
Show answers
- 0.00605
- 3.05 × 10⁻⁴
- 4 × 10⁴
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