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Standard form (scientific notation): write and calculate

Write very large and very small numbers in standard form, convert them back and multiply them, with worked examples for GCSE and high school.

IntermediateUpdated 5 Nov 2026
GCSEHigh School

Curriculum fit: GCSE Maths Number (Foundation and Higher). US: Grade 8 scientific notation, used in high school science.

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What is it?

Standard form, called scientific notation in the US, is a way of writing very large or very small numbers compactly. A number is in standard form when it is written as A × 10ⁿ, where A is at least 1 and less than 10, and n is a whole number.

For example, the speed of light is about 300 000 000 m/s, which is 3 × 10⁸ m/s. A tiny length such as 0.000 004 m is 4 × 10⁻⁶ m.

Key formulas and ideas

  • Standard form: A × 10ⁿ with 1 ≤ A < 10 and n a whole number.
  • Large numbers have positive n. Numbers between 0 and 1 have negative n.
  • Multiplying: multiply the A parts and add the powers of 10. Dividing: divide the A parts and subtract the powers.

Worked examples

Example 1: Large number

Question: Write 45 600 000 in standard form.

  1. Place the decimal point after the first digit: 4.56.
  2. Count how many places it moved: 7.
  3. So the number is 4.56 × 10⁷.

Answer: 4.56 × 10⁷

Example 2: Small number

Question: Write 0.000 032 in standard form.

  1. Move the decimal point to get 3.2.
  2. It moved 5 places to the right, so the power is −5.

Answer: 3.2 × 10⁻⁵

Example 3: Multiplying

Question: Work out (3 × 10⁴) × (2 × 10⁵).

  1. Multiply 3 × 2 = 6.
  2. Add the powers: 4 + 5 = 9.

Answer: 6 × 10⁹

Common mistakes

  • Leaving A outside the range 1 to 10, such as 45 × 10⁶.
  • Using a positive power for a small number.
  • Counting the decimal places wrongly.
  • After multiplying, forgetting to adjust when the A part becomes 10 or more: 12 × 10⁵ must become 1.2 × 10⁶.

Practice questions

1. Write 7 200 000 in standard form.
2. Write 0.0009 in standard form.
3. Write 5.1 × 10³ as an ordinary number.
4. Work out (4 × 10³) × (3 × 10⁴).
5. Which of these numbers has the greatest value?

Frequently asked questions

How do I enter standard form on a calculator?

Use the EXP or ×10ˣ button. Check your calculator's instructions, because the key differs between models.

Why is standard form useful?

It keeps very large and very small numbers short, and makes them easy to compare and multiply.

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Sources and review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.