IGCSE Maths Standard Form Notes
Standard form writes numbers as A × 10ⁿ, making very large and very small values easy to write and calculate with.
Key concepts
- Format
- A × 10ⁿ where 1 ≤ A < 10 and n is an integer.
- Positive power
- n > 0 for large numbers — move the decimal point right.
- Negative power
- n < 0 for small numbers — move the decimal point left.
Key formulas
Multiplying
(A × 10ᵐ)(B × 10ⁿ) = AB × 10ᵐ⁺ⁿ
Dividing
(A × 10ᵐ) ÷ (B × 10ⁿ) = (A/B) × 10ᵐ⁻ⁿ
Worked example
Work out (3 × 10⁵) × (2 × 10³).
- 1Multiply the numbers: 3 × 2 = 6.
- 2Add the powers: 10⁵ × 10³ = 10⁸.
- 3Combine: 6 × 10⁸.
Answer: 6 × 10⁸
Common mistakes
✗ Leaving an answer like 12 × 10⁴.
✓ Adjust so 1 ≤ A < 10: 1.2 × 10⁵.
✗ Adding powers when dividing.
✓ Subtract powers when dividing, add when multiplying.
✗ Wrong sign on the power for small numbers.
✓ Numbers below 1 have a negative power.
Quick check
Try these, then reveal the answers.
Write 6 200 000 in standard form.Reveal answer
6.2 × 10⁶
(4 × 10⁶) ÷ (2 × 10²) = ?Reveal answer
2 × 10⁴
Write 5 × 10⁻³ as an ordinary number.Reveal answer
0.005
Exam tips
- Always re-check that A lies between 1 and 10 after calculating.
- Use the ×10ˣ (or EXP) key rather than typing 'x10^'.
- For addition and subtraction, convert to the same power first.
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Frequently asked questions
Why use standard form?+
It keeps very large or very small numbers short and makes multiplying and dividing them straightforward using index laws.
How do I add numbers in standard form?+
Convert them to the same power of 10 (or to ordinary numbers), add, then rewrite in standard form.
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