Standard form

Standard form writes very big or very small numbers neatly as A × 10ⁿ, where A is at least 1 and less than 10. Big numbers have a positive power; small numbers (less than 1) have a negative power.

Key facts

  • A must be at least 1 and less than 10.
  • Count how many places the decimal point moves: that is n.
  • Numbers bigger than 10: n is positive. Numbers less than 1: n is negative.
  • To multiply, multiply the A parts and add the powers.

Worked examples

Example 1

Write 4 300 000 in standard form.

  1. Put the point after the first digit. 4.3
  2. It moved 6 places to the left. 4 300 000 = 4.3 × 10⁶

Answer: 4.3 × 10⁶

Example 2

Write 0.00072 in standard form.

  1. Put the point after the first non-zero digit. 7.2
  2. It moved 4 places to the right, so the power is negative. 7.2 × 10⁻⁴

Answer: 7.2 × 10⁻⁴

Example 3

Work out (3 × 10⁴) × (5 × 10³) in standard form.

  1. Multiply the numbers. 3 × 5 = 15
  2. Add the powers. 10⁴ × 10³ = 10⁷
  3. 15 isn’t less than 10, so adjust. 15 × 10⁷ = 1.5 × 10⁸

Answer: 1.5 × 10⁸