Standard Form (Copy)

IGCSE CORE Mathematics Cheat Sheet: Standard Form (Scientific Notation)

1. What is Standard Form?

• Standard Form (also called Scientific Notation) is a way of writing very large or very small numbers.
• The format is:
  A × 10ⁿ, where:
  • 1 ≤ A < 10
  • n is an integer (can be positive or negative)

2. When to Use Standard Form

• For very large numbers:
  Example: 300,000,000 → 3 × 10⁸
• For very small numbers:
  Example: 0.00042 → 4.2 × 10⁻⁴

3. Converting Numbers Into Standard Form

• Large Numbers (n is positive):
  1. Place decimal after the first non-zero digit.
  2. Count how many places you move the decimal → that’s n.

  Example:
  72,000 = 7.2 × 10⁴

• Small Numbers (n is negative):
  1. Place decimal after the first non-zero digit.
  2. Count how many places you move the decimal → n is negative.

  Example:
  0.0051 = 5.1 × 10⁻³

4. Converting From Standard Form to Ordinary Numbers

• Positive n: Move decimal right.
  Example: 4.3 × 10³ = 4300
• Negative n: Move decimal left.
  Example: 6.2 × 10⁻² = 0.062

5. Calculations with Standard Form

(Paper 3 Only)

• Multiplication:
  Multiply A-values, add powers of 10.
  Example:
  (3 × 10²) × (4 × 10³) = (3×4) × 10²⁺³ = 12 × 10⁵
  Adjust to standard form: 1.2 × 10⁶
• Division:
  Divide A-values, subtract powers of 10.
  Example:
  (6 × 10⁵) ÷ (2 × 10²) = (6÷2) × 10⁵⁻² = 3 × 10³
• Addition/Subtraction:
  Make powers of 10 the same, then add/subtract A-values.

Example:
(5.4 × 10³) + (3.1 × 10²)
= (5.4 × 10³) + (0.31 × 10³)
= 5.71 × 10³

6. Examples

• Convert 58,000 to standard form:
  = 5.8 × 10⁴
• Convert 0.00072 to standard form:
  = 7.2 × 10⁻⁴
• Write 3.6 × 10² as an ordinary number:
  = 360
• Calculate:
  (2 × 10³) × (5 × 10²) = 1.0 × 10⁶
• Calculate:
  (4.8 × 10⁵) ÷ (1.6 × 10²) = 3 × 10³

7. Quick Reference Table

8. Tips for Exams

• Always check 1 ≤ A < 10 after calculations—adjust if necessary.
• For multiplication/division, handle numbers and powers separately.
• For addition/subtraction, powers of 10 must be equal before calculating.
• Don’t forget to rearrange answers back into proper standard form if A goes above 10.
• Use your calculator’s standard form mode efficiently on Paper 3.