Knowledge Organiser: Standard Form
Part of Standard Form · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Standard Form within Standard Form for GCSE Mathematics. Revise Standard Form in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 15 of 15 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 15 of 15
Practice
14 questions
Recall
22 flashcards
Knowledge Organiser: Standard Form
Key Terms
- Standard form: A number written as a × 10ⁿ where 1 ≤ a < 10
- Coefficient (a): Must be at least 1 and less than 10
- Power (n): Positive for large numbers, negative for small numbers
- Scientific notation: Alternative name for standard form
Must-Know Facts
- a must satisfy: 1 ≤ a < 10 (e.g. 45 × 10³ is NOT valid — should be 4.5 × 10⁴)
- Large number → positive power (decimal moved left)
- Small number → negative power (decimal moved right)
- 3.2 × 10⁻³ = 0.0032 (negative means small, not negative number)
- Multiply: multiply coefficients, add powers
- Divide: divide coefficients, subtract powers
- Add/subtract: convert to same power first
Key Formulas
- a × 10ⁿ where 1 ≤ a < 10
- (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ
- (a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ
- Speed of light = 3 × 10⁸ m/s (real-world example)
Common Mistakes
- a not between 1 and 10: 32 × 10⁴ is not standard form — must be 3.2 × 10⁵
- Direction of index: Large numbers use positive powers; small decimals use negative powers
- Adding in standard form: Convert to ordinary numbers first (or ensure same power of 10)
- Multiplying indices: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷ — add the indices, don't multiply them
- Calculator display: 3.2E5 on a calculator means 3.2 × 10⁵ — always write out the full form in answers
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Read this section alongside the surrounding pages in Standard Form. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Standard Form
Which of these numbers is written in standard form?
Explain why standard form is useful for writing very large or very small numbers.
Quick Recall Flashcards
14 questions on Standard Form — practise free
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