Standard Form

O Level and IGCSE Mathematics Cheat Sheet – 1.8 Standard Form

Definition

• Standard form (scientific notation) is written as:
  A × 10ⁿ
  • 1 ≤ A < 10 (A can be a decimal)
  • n is an integer (positive, negative, or zero)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Why Use Standard Form?

• Makes it easier to write and work with very large or very small numbers.
• Common in science, engineering, and astronomy.

Converting to Standard Form

1. Move decimal point so that A is between 1 and 10.
2. Count number of places moved = exponent (n).
3. If moved left, n is positive.
4. If moved right, n is negative.

Examples:

• 3,500 = 3.5 × 10³
• 0.0042 = 4.2 × 10⁻³

Converting from Standard Form

• If n is positive → move decimal right n places.
• If n is negative → move decimal left |n| places.

Examples:

• 6.1 × 10⁴ = 61,000
• 2.8 × 10⁻² = 0.028

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Calculations in Standard Form

Multiplication:

• Multiply A values.
• Add powers of 10.
  Example: (3 × 10⁵) × (2 × 10³) = (6) × 10⁸

Division:

• Divide A values.
• Subtract powers of 10.
  Example: (8 × 10⁶) ÷ (4 × 10²) = (2) × 10⁴

Addition / Subtraction:

• First make powers of 10 the same, then add/subtract A values.
  Example: (5.2 × 10³) + (4.8 × 10²)
  = (5.2 × 10³) + (0.48 × 10³) = 5.68 × 10³

Exam Special Tips

• Always adjust final answer so 1 ≤ A < 10.
• When adding/subtracting, align exponents first.
• Watch out for calculator output in E notation: 4.2E5 = 4.2 × 10⁵.
• For accuracy, keep A to the required significant figures.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Common Mistakes & Confusions

• Writing A ≥ 10 or A < 1 — not allowed in standard form.
• Forgetting to change A after multiplication/division if it’s outside range.
• Mixing up sign of exponent when converting from decimals.
• Adding/subtracting without matching powers of 10.