Lesson 1: Understanding Numbers in IGCSE Mathematics – The Foundation of Success

Mathematics begins with numbers. In IGCSE Mathematics, mastering the basics of numbers is the first step toward building confidence and scoring well in exams. This lesson will guide you through the essential number concepts you must know.

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🔹 1. Place Value and Standard Form

Place Value:
Every digit in a number has a value depending on its position. For example:

• In 4,582,

  • 4 → Thousands

  • 5 → Hundreds

  • 8 → Tens

  • 2 → Units

Standard Form (Scientific Notation):
A way to write very large or very small numbers.

👉 Formula:

$$a \times 10^n \quad \text{where } 1 \leq a < 10$$

Examples:

• 45,000 = $4.5 \times 10^4$

• 0.0062 = $6.2 \times 10^{-3}$

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🔹 2. Prime Numbers, Factors, and Multiples

• Prime Number → A number with exactly two factors (1 and itself).
  Examples: 2, 3, 5, 7, 11, 13 …

• Factors → Numbers that divide exactly into another number.
  Example: Factors of 12 → 1, 2, 3, 4, 6, 12

• Multiples → Products of a number.
  Example: Multiples of 4 → 4, 8, 12, 16 …

Exam Tip: Learn prime numbers up to 50 – they often appear in factorization questions.

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🔹 3. Highest Common Factor (HCF) & Lowest Common Multiple (LCM)

• HCF: The biggest number that divides exactly into two numbers.

• LCM: The smallest number that is a multiple of both numbers.

Example:
Find the HCF and LCM of 18 and 24.

• 18 = 2 × 3²

• 24 = 2³ × 3

👉 HCF = 2 × 3 = 6
👉 LCM = 2³ × 3² = 72

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🔹 4. Types of Numbers in IGCSE Mathematics

• Integers → Whole numbers (… -3, -2, -1, 0, 1, 2 …)

• Rational Numbers → Fractions & decimals that can be written as $\frac{p}{q}$.

• Irrational Numbers → Numbers that cannot be written as fractions (e.g. √2, π).

• Real Numbers → All of the above combined.

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🔹 5. Practice Questions

Try these questions (answers below 👇):

1. Write 0.00054 in standard form.

2. List all prime numbers between 20 and 30.

3. Find the HCF and LCM of 30 and 45.

4. Classify each number as integer, rational, or irrational:

   • 7, 0.25, √3, -12

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✅ Answers

1. $5.4 \times 10^{-4}$

2. 23, 29

3. • 30 = 2 × 3 × 5

   • 45 = 3² × 5

   • HCF = 15

   • LCM = 90

4. • 7 → Integer, Rational

   • 0.25 → Rational

   • √3 → Irrational

   • -12 → Integer, Rational