GCSE Maths Number Notes
Number underpins the whole GCSE Maths paper. Confidence with fractions, percentages, indices and rounding earns quick, reliable marks throughout.
Key concepts
- Place value
- The value of a digit depends on its position — the 3 in 3200 is worth 3000. Vital for standard form and rounding.
- Factors and multiples
- Factors divide into a number exactly; multiples are the times-table. HCF and LCM come from prime factors.
- Indices
- A power tells you how many times to multiply a number by itself, e.g. 2⁴ = 16.
- Surds
- Roots that cannot be simplified to a whole number, e.g. √2. Leave them exact rather than rounding.
- To find the HCF and LCM, write each number as a product of prime factors first.
- Multiplying by a number less than 1 makes the result smaller — a common surprise.
- Percentages, decimals and fractions are three ways of writing the same amount.
Key formulas
Index laws
aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ
Percentage of an amount
value = (percentage ÷ 100) × amount
Worked example
Increase £80 by 15%.
- 1Find 15% of 80: 0.15 × 80 = 12.
- 2Add it to the original: 80 + 12 = 92.
- 3Or use a multiplier: 80 × 1.15 = 92.
Answer: £92
Common mistakes
✗ Adding percentages of different totals, e.g. treating 10% of £50 and 10% of £80 as equal.
✓ Always take the percentage of the correct amount before comparing.
✗ Rounding surds too early.
✓ Keep answers as exact surds (e.g. 2√3) until the very end unless told to round.
✗ Writing 3⁰ = 0.
✓ Any non-zero number to the power 0 equals 1.
Quick check
Try these, then reveal the answers.
Work out 30% of 150.Reveal answer
45
Simplify 2³ × 2².Reveal answer
2⁵ = 32
Write 0.25 as a fraction.Reveal answer
1/4
Exam tips
- For percentage change, learn the multiplier method — it is faster and reduces errors.
- Show prime factor trees for HCF/LCM questions to secure method marks.
- On the non-calculator paper, leave surds and π exact rather than as decimals.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
What is a multiplier in percentages?+
A decimal you multiply by to change an amount — 1.15 for a 15% increase, 0.85 for a 15% decrease.
What is the difference between HCF and LCM?+
The HCF is the largest number that divides into all of them; the LCM is the smallest number they all divide into.
Create a free account to practise number with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.