Topic 1 of 11 · Form 1
Number: types, factors, standard form and bounds
Natural numbers, integers, prime numbers, square and cube numbers, rational and irrational numbers (√2, π), reciprocals.
Notes for this topic 1 file, in order
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Types of number
Natural numbers, integers, prime numbers, square and cube numbers, rational and irrational numbers (√2, π), reciprocals.
Factors and multiples
Write numbers as products of prime factors to find the HCF and LCM.
Worked example: Find the HCF and LCM of 84 and 120.
84 = 2² × 3 × 7; 120 = 2³ × 3 × 5
HCF = 2² × 3 = 12; LCM = 2³ × 3 × 5 × 7 = 840
Standard form
A × 10ⁿ with 1 ≤ A < 10. 0.000 46 = 4.6 × 10⁻⁴.
Accuracy and bounds
Round to decimal places or significant figures. A value rounded to the nearest unit lies within half a unit: 7 cm (nearest cm) has lower bound 6.5 cm and upper bound 7.5 cm. For calculations, combine bounds to find the extremes (e.g. maximum of a ÷ b = upper a ÷ lower b).
Worked example: A rectangle is 8 cm by 5 cm, each to the nearest cm. Find the upper bound of its area.
8.5 × 5.5 = 46.75 cm²
Estimation
Round each number to 1 significant figure to check answers.
Check yourself
- Write 36 000 000 in standard form.
- Is √49 rational or irrational?
- Find the LCM of 12 and 18.
Show answers
- 3.6 × 10⁷
- Rational (it equals 7).
- 36
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