Summary
This topic covers various aspects of numbers, including integers, highest common factors (HCF), lowest common multiples (LCM), prime numbers, rational and irrational numbers, significant figures, and decimal places.
- Integers — whole numbers that can be positive, negative, or zero. Example: -3, 0, 4
- HCF/LCM — HCF is the largest number that divides two or more numbers, while LCM is the smallest number that is a multiple of two or more numbers. Example: HCF of 12 and 18 is 6; LCM of 12 and 18 is 36
- Prime Numbers — numbers greater than 1 that have no divisors other than 1 and themselves. Example: 2, 3, 5, 7
- Rational Numbers — numbers that can be expressed as a fraction of two integers. Example: 1/2, 3.75
- Irrational Numbers — numbers that cannot be expressed as a simple fraction. Example: √2, π
- Significant Figures — digits in a number that contribute to its accuracy. Example: 123.45 to 3 significant figures is 123
- Decimal Places — the number of digits to the right of the decimal point. Example: 3.456 to 2 decimal places is 3.46
Exam Tips
Key Definitions to Remember
- Integers are whole numbers, including negatives and zero.
- HCF is the greatest number that divides two numbers.
- LCM is the smallest common multiple of two numbers.
- Prime numbers have only two divisors: 1 and themselves.
- Rational numbers can be expressed as fractions.
- Irrational numbers cannot be expressed as simple fractions.
- Significant figures are the digits that carry meaning in a number.
- Decimal places refer to the digits after the decimal point.
Common Confusions
- Confusing HCF with LCM.
- Misidentifying prime numbers.
- Mixing up rational and irrational numbers.
Typical Exam Questions
- What is the HCF of 45 and 105? Answer: 15
- Write 3.5897 correct to 4 significant figures. Answer: 3.590
- Find the LCM of 36 and 48. Answer: 144
What Examiners Usually Test
- Ability to find HCF and LCM.
- Identification of prime numbers.
- Conversion between significant figures and decimal places.