Revising standard form the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Standard form GCSE” on the site for the complete guide.
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Key facts to remember
1Standard form: A × 10ⁿ where 1 ≤ A < 10 and n is an integer.
2Positive powers of 10 → large numbers (move decimal right).
3Negative powers of 10 → small numbers (move decimal left).
4To multiply in standard form: multiply the A values and add the powers.
5To divide in standard form: divide the A values and subtract the powers.
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Formulas
Multiply
(A × 10ᵐ) × (B × 10ⁿ) = AB × 10^(m+n)
Divide
(A × 10ᵐ) ÷ (B × 10ⁿ) = (A/B) × 10^(m−n)
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Worked examples
Example 1
Write 0.000034 in standard form.
Working
Move the decimal point to get a number between 1 and 10: 3.4
Count how many places the decimal moved: 5 places to the right
So the power is −5
Answer3.4 × 10⁻⁵
Example 2
Work out (3 × 10⁴) × (2 × 10³)
Working
Multiply the numbers: 3 × 2 = 6
Add the powers: 4 + 3 = 7
= 6 × 10⁷
Answer6 × 10⁷
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Common mistakes
✗Writing A as a number ≥ 10 or < 1 (e.g. 34 × 10⁻⁶ is not standard form).
✗Subtracting instead of adding powers when multiplying.
✗Forgetting to adjust A back to the range 1–10 after calculating.
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Exam tips
✓After any calculation, always check that A is between 1 and 10.
✓On a calculator, use the EXP or ×10ˣ button — don't type × 10 separately.
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