GCSE Maths Standard Form Notes
Standard form writes very large or very small numbers compactly as A × 10ⁿ, where 1 ≤ A < 10. It keeps big and tiny numbers manageable.
Key concepts
- Standard form
- A number written as A × 10ⁿ where A is between 1 and 10 (including 1) and n is an integer.
- Positive power
- Large numbers have a positive n: 4 500 = 4.5 × 10³.
- Negative power
- Small numbers have a negative n: 0.0032 = 3.2 × 10⁻³.
Key formulas
Standard form
A × 10ⁿ, 1 ≤ A < 10
n is a whole number, positive or negative.
Worked example
Write 0.00047 in standard form.
- 1Place the decimal point after the first non-zero digit: 4.7.
- 2Count how many places it moved: 4 places right.
- 3Because the number is small, the power is negative: 4.7 × 10⁻⁴.
Answer: 4.7 × 10⁻⁴
Common mistakes
✗ Writing A outside the range, e.g. 47 × 10³.
✓ A must be at least 1 and less than 10 — adjust to 4.7 × 10⁴.
✗ Getting the sign of the power wrong.
✓ Big numbers → positive power; small (decimal) numbers → negative power.
✗ Adding the powers when multiplying without handling the digits.
✓ Multiply the A parts, add the powers, then fix A back into range.
Quick check
Try these, then reveal the answers.
Write 62 000 in standard form.Reveal answer
6.2 × 10⁴
Write 5.4 × 10⁻² as an ordinary number.Reveal answer
0.054
Is 12 × 10³ in standard form?Reveal answer
No — A must be less than 10.
Exam tips
- On a calculator, use the ×10ˣ (or EXP) button, not the ^ key, to avoid errors.
- When adding or subtracting, convert to ordinary numbers first or match the powers.
- Always check A is between 1 and 10 in your final answer.
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Frequently asked questions
How do I multiply numbers in standard form?+
Multiply the A values, add the powers of 10, then adjust so A is between 1 and 10.
Why do we use standard form?+
It writes very large or very small numbers compactly and makes calculating with them far easier.
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