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Number · Foundation & Higher

Standard form

Standard form (scientific notation) is a way of writing very large or very small numbers using powers of 10.

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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

  1. Move the decimal point to get a number between 1 and 10: 3.4
  2. Count how many places the decimal moved: 5 places to the right
  3. So the power is −5
Answer3.4 × 10⁻⁵
Example 2

Work out (3 × 10⁴) × (2 × 10³)

Working

  1. Multiply the numbers: 3 × 2 = 6
  2. Add the powers: 4 + 3 = 7
  3. = 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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