GCSERevise
AQASpec N1-N2Foundation & Higher~25 min

Integers, Decimals & Place Value

Mathematics · Topic revision workspace

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Read the notes, score 80% and know 75% of the cards.

Topic overview

What you need to know

Integers, Decimals & Place Value is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A whole number that can be positive, negative, or zero (e.g. -3, 0, 7). The value of a digit determined by its position in a number. For example, in 345 the 3 represents 300. The order of operations: Brackets, Indices (or Orders), Division, Multiplication, Addition, Subtraction.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Integer: A whole number that can be positive, negative, or zero (e.g. -3, 0, 7).
  • Place Value: The value of a digit determined by its position in a number. For example, in 345 the 3 represents 300.
  • BIDMAS/BODMAS: The order of operations: Brackets, Indices (or Orders), Division, Multiplication, Addition, Subtraction.
  • Factor: A whole number that divides exactly into another number with no remainder. E.g. factors of 12 are 1, 2, 3, 4, 6, 12.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Multiple: The result of multiplying a number by any positive integer. E.g. multiples of 5 are 5, 10, 15, 20, …
  • Prime Number: A number greater than 1 that has exactly two factors: 1 and itself. E.g. 2, 3, 5, 7, 11.
  • LCM (Lowest Common Multiple): The smallest number that is a multiple of two or more given numbers. E.g. LCM of 4 and 6 is 12.
  • HCF (Highest Common Factor): The largest number that divides exactly into two or more given numbers. E.g. HCF of 12 and 18 is 6.

Core knowledge

Key facts for Integers, Decimals & Place Value

1

Integer

A whole number that can be positive, negative, or zero (e.g. -3, 0, 7).

2

Place Value

The value of a digit determined by its position in a number. For example, in 345 the 3 represents 300.

3

BIDMAS/BODMAS

The order of operations: Brackets, Indices (or Orders), Division, Multiplication, Addition, Subtraction.

4

Factor

A whole number that divides exactly into another number with no remainder. E.g. factors of 12 are 1, 2, 3, 4, 6, 12.

5

Multiple

The result of multiplying a number by any positive integer. E.g. multiples of 5 are 5, 10, 15, 20, …

6

Prime Number

A number greater than 1 that has exactly two factors: 1 and itself. E.g. 2, 3, 5, 7, 11.

7

LCM (Lowest Common Multiple)

The smallest number that is a multiple of two or more given numbers. E.g. LCM of 4 and 6 is 12.

8

HCF (Highest Common Factor)

The largest number that divides exactly into two or more given numbers. E.g. HCF of 12 and 18 is 6.

Active recall

Close the notes and answer these

  1. 1.Without looking, explain integer and give one example or consequence.
  2. 2.Without looking, explain place value and give one example or consequence.
  3. 3.Without looking, explain bidmas/bodmas and give one example or consequence.
  4. 4.Without looking, explain factor and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

Official AQA specification
Next topicFractions, Decimals & Percentages