Types of numbers
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Statistics
Sets and Venn diagrams
Sampling and bias
Collecting data: types and classes of data
Mean, median, mode and range
Simple charts and graphs
Pie charts
Scatter graphs
Frequency tables: finding averages
Grouped frequency tables
Box plots - Higher
Cumulative frequency - Higher
Histograms and frequency density - Higher
Interpreting data
Comparing data sets
Probability
Trigonometry
Angles and geometry
Shapes and area
Properties of 2D shapes
Congruence: conditions for congruent triangles
Similar shapes: Scaling
The four transformations
Area and perimeter: Formulae
Area and circumference of circles: Formulae
3D shapes: faces, edges, vertices
Surface area of 3D shapes: Nets, formulae
Volume of 3D shapes: Formulae
Volume of 3D shapes: Comparing, rates of flow
Area and volume scale factors
Projections and elevations of 3D shapes
Ratio proportion and rates of change
Graphs
Coordinates and midpoints
Straight line graphs
Drawing straight line graphs
Finding the gradient of a straight line
Equation of a straight line: y = mx + c
Coordinates and ratio
Parallel and perpendicular lines
Quadratic graphs
Reciprocal and cubic graphs
Exponential graphs and circles - Higher
Trigonometric graphs - Higher
Solving equations using graphs
Graph transformations - Higher
Real-life graphs
Distance-time graphs
Velocity-time graphs - Higher
Gradients of real-life graphs - Higher
Algebra
Simplifying algebraic expressions
Multiplying and dividing algebraic expressions
Single brackets: Expanding and factorising
Double brackets: Expanding and factorising
Double and triple brackets - Higher
Solving equations
Expressions, equations, formulae, functions and identities
Writing formulae and equations from word problems
Writing formulae and equations from diagrams
Rearranging formulae
Factorising quadratics
The quadratic formula - Higher
Complete the square - Higher
Algebraic fractions - Higher
Sequences
Finding the nth term
Solving inequalities
Inequalities on graphs - Higher
Iteration - Higher
Simultaneous equations: elimination and substitution
Non-linear simultaneous equations - Higher
Algebraic proof - Higher
Composite and inverse functions - Higher
Number
Types of numbers
Order of operations: BODMAS
Multiplying and dividing by powers of 10
Multiplying and dividing whole numbers
Multiplying and dividing decimals
Negative numbers: add, subtract, multiply, divide
Prime numbers and prime factorisation
Multiples, factors and prime factors
LCM and HCF
Fractions
Fractions, decimals and percentages
Writing recurring decimals as fractions
Rounding: Integers, decimal places, significant figures
Estimation
Error intervals
Upper and lower bounds - Higher
Powers and roots: Square and cube numbers
Laws of indices: multiply, divide, brackets
Index laws: negative and fractional indices - Higher
Surds: Simplify, add and subtract - Higher
Rationalising surds - Higher
Standard form calculations
Explainer Video
Summary
Types of numbers
In a nutshell
Numbers are used to represent quantities of items, and different types of numbers belong to different sets. For example, integers can be used for counting while rational numbers are better used to describe how much of a portion remains.
Identifying types of numbers
Type | Description | Example |
Natural | Any positive whole number is a natural number (not including ) | |
Integer | Any whole number is an integer (including ) | |
Rational | Any number that can be expressed as a fraction where in its simplest form both the numerator and denominator are integers | |
Irrational | Any number that cannot be expressed as a fraction | |
Real | Any number is a real number | |
Prime | Any positive whole number that has only two factors, that being and itself | |
Square | Any number that can be expressed as the square of a natural number | |
Cube | Any number that can be expressed as the cube of a natural number | |
Surd | Square rooted numbers and can be positive or negative | |
Example 1
What type of number is ?
Hence as this is the simplest form and both the numerator and denominator are integers, is a rational number.
Subsets of numbers
Some of the definitions of numbers overlap. For instance, falls into the category of a natural number, integer, rational number and also a real number. This gives a subset order for the types of numbers which can be seen below:
From the Venn diagram you can see that all natural numbers are integers, all integers are rational numbers, and all rational and irrational numbers are real.
FAQs - Frequently Asked Questions
How do I determine what type a number is?
Match the number to the definition of the number and then show that the number fits the definition.
What are the 7 types of numbers?
Integer, rational, irrational, prime, square, cube, surd.
What is a rational number?
Numbers that can be written as fractions, where both the numerator and denominator are integers.
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