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Types of numbers

Types of numbers

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Basics of probability

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Vectors - Higher

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Ratio

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Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

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Double and triple brackets - Higher

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Writing formulae and equations from word problems

Writing formulae and equations from diagrams

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Complete the square - Higher

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Sequences

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Iteration - Higher

Simultaneous equations: elimination and substitution

Non-linear simultaneous equations - Higher

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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

Tutor: Alice

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 000)​
​1,2,51, 2,51,2,5​​
Integer
Any whole number is an integer (including 000)​
​0,7,−30,7, -30,7,−3​​
Rational
Any number that can be expressed as a fraction where in its simplest form both the numerator and denominator are integers
​167,−13,9\dfrac{16}{7}, -\dfrac{1}{3}, 9716​,−31​,9​​
Irrational
Any number that cannot be expressed as a fraction
​π,2,173\pi, \sqrt{2}, \sqrt{\dfrac{17}{3}}π,2​,317​​​​
Real
Any number is a real number
​3,4,−35\sqrt{3}, 4, -\dfrac{3}{5}3​,4,−53​​​
Prime
Any positive whole number that has only two factors, that being 111 and itself​
​2,5,132,5,132,5,13​​
Square
Any number that can be expressed as the square of a natural number
​1,4,161, 4, 161,4,16​​
Cube
Any number that can be expressed as the cube of a natural number
​1,−8,271, -8,271,−8,27​​
Surd
Square rooted numbers and can be positive or negative
​50, 346, −8\sqrt{50},\, 3\sqrt46,\, -\sqrt{8}50​,34​6,−8​​​


Example 1

What type of number is 8.68.68.6?

 8.6=8610=4358.6 = \dfrac{86}{10} = \dfrac{43}{5}8.6=1086​=543​


Hence as this is the simplest form and both the numerator and denominator are integers, 8.68.68.6 is a rational number.



Subsets of numbers

Some of the definitions of numbers overlap. For instance, 666 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:


Maths; Number; KS4 Year 10; Types of numbers


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.


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Prime numbers, prime factors and composite numbers

Prime numbers, prime factors and composite numbers

Special types of numbers

Special types of numbers

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Types of numbers

Types of numbers

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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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