Indices & Standard Form — GCSE Mathematics Revision
Revise Indices & Standard Form for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to SurdsWhat is Indices & Standard Form?
Index laws let you simplify expressions with powers. Standard form writes very large or small numbers as A × 10ⁿ where 1 ≤ A < 10. For example, 45,000 = 4.5 × 10⁴ and 0.003 = 3 × 10⁻³. You need to add, subtract, multiply and divide numbers in standard form, and convert between standard form and ordinary numbers.
Board notes: Standard form appears on both tiers. Negative and fractional indices are Higher only.
Step-by-step explanationWorked example
Write 0.00056 in standard form. Move the decimal 4 places right: 5.6 × 10⁻⁴.
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Common mistakes
- 1Writing A outside the range 1 ≤ A < 10 (e.g. 45 × 10³ is not standard form).
- 2Getting the sign of the power wrong — large numbers have positive powers, small decimals have negative powers.
- 3Not adjusting the power of 10 when adding/subtracting numbers in standard form with different powers.
- 4Confusing negative indices with negative numbers: 2⁻³ = 1/8, not -8.
Indices & Standard Form exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Indices & Standard Form
Core concept
Index laws let you simplify expressions with powers. Standard form writes very large or small numbers as A × 10ⁿ where 1 ≤ A < 10. For example, 45,000 = 4.5 × 10⁴ and 0.003 = 3 × 10⁻³. You need to add…
Frequently asked questions
How do I multiply numbers in standard form?
Multiply the A values together and add the powers of 10. If the result for A is ≥ 10, adjust by dividing by 10 and adding 1 to the power. Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
What does a negative index mean?
A negative index means the reciprocal: a⁻ⁿ = 1/aⁿ. For example, 5⁻² = 1/25. It does NOT mean the number is negative.