What is important to know about Standard form?

Standard form: A × 10ⁿ where 1 ≤ A < 10 and n is an integer.

What is important to know about Standard form?

Positive powers of 10 → large numbers (move decimal right).

What is important to know about Standard form?

Negative powers of 10 → small numbers (move decimal left).

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Number · Foundation & Higher

Standard form

Q: What is important to know about Standard form?

Positive powers of 10 → large numbers (move decimal right).

Q: What is important to know about Standard form?

Negative powers of 10 → small numbers (move decimal left).

Q: What are common mistakes with Standard form?

Writing A as a number ≥ 10 or < 1 (e.g. 34 × 10⁻⁶ is not standard form).

Q: What are common mistakes with Standard form?

Subtracting instead of adding powers when multiplying.

Q: What exam tips are there for Standard form?

After any calculation, always check that A is between 1 and 10.

Q: What exam tips are there for Standard form?

On a calculator, use the EXP or ×10ˣ button — don't type × 10 separately.

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

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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