Number
Choose your practice ↓Number is where most of the arithmetic that the rest of the paper depends on lives. It runs from ordering positive and negative integers, decimals and fractions, through the four operations by formal written method, to factors, multiples, the highest common factor and the lowest common multiple, and on to indices, standard form, rounding to a given number of significant figures, and error intervals. Higher adds surds — simplifying them and rationalising denominators — fractional and negative indices, converting a recurring decimal to a fraction, and upper and lower bounds. Number is worth 25% of the Foundation paper and 15% of Higher, but its real weight is larger than either figure suggests: a ratio question you cannot finish because of the fraction arithmetic in it is lost on number, not on ratio. Most of this content is at its hardest on Paper 1, where there is no calculator to fall back on.
📚 What you learn here
- Ordering integers, decimals and fractions, and using =, ≠, <, >, ≤, ≥
- The four operations with negatives, decimals, improper fractions and mixed numbers, by formal written method
- Priority of operations: brackets, indices, roots and reciprocals
- Prime factorisation, and finding the highest common factor and lowest common multiple from it
- Powers and roots, the laws of indices, and (Higher) fractional and negative indices
- Surds: simplifying √12 to 2√3 and rationalising a denominator (Higher)
- Standard form A × 10ⁿ, including calculating with it
- Terminating and recurring decimals and their fractions (recurring to fraction is Higher)
- Rounding to decimal places and significant figures, estimation, error intervals, and upper and lower bounds (Higher)
Frequently asked questions
What is the difference between the HCF and the LCM?
The highest common factor is the largest number that divides into both numbers; the lowest common multiple is the smallest number both numbers divide into. From a prime factorisation, the HCF takes the lower power of each shared prime and the LCM takes the higher power of every prime that appears. If you answer with a number smaller than both originals for an LCM, you have swapped them.
Do I need to know surds for Foundation?
No. Surds and rationalising denominators are Higher only. Foundation calculates exactly with fractions and multiples of π, but not with surds.
How do I write a number in standard form?
As A × 10ⁿ where A is at least 1 and less than 10 and n is an integer. So 4300 is 4.3 × 10³ and 0.00062 is 6.2 × 10⁻⁴. A written as 43 or 0.62 is the most common lost mark here.
Which number topics come up on the non-calculator paper?
Nearly all of them. Ordering, the four operations, order of operations, factors and multiples, indices, surds, fraction and decimal conversion and estimation are all natural Paper 1 material. Bounds and some standard form work sit more comfortably on a calculator paper.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications