Edexcel International GCSE Mathematics A · 4MA1
Standard form
Standard form expresses a non-zero number as a × 10ⁿ with 1 ≤ |a| < 10 and integer n. It makes very large or small quantities easier to compare and calculate with. The coefficient must be normalised after arithmetic.
Key method
When multiplying, multiply the coefficients and add the powers. When dividing, divide coefficients and subtract powers. Adjust the coefficient back into the required range.
Worked example
Calculate (6 × 10⁵)(4 × 10⁻³) in standard form.
- Multiply the coefficients: 6 × 4 = 24.
- Add the powers: 5 + (−3) = 2, giving 24 × 10².
- Rewrite 24 as 2.4 × 10, increasing the power by 1.
Answer and interpretation
2.4 × 10³.
Common mistake
Leaving 24 × 10² is numerically correct but is not standard form.
Practise independently
Write 0.000072 in standard form.
Check your answer
7.2 × 10⁻⁵; a negative exponent represents a small positive number here.
Syllabus connection
This lesson develops standard form within the number area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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