Types of Number (Edexcel GCSE Maths): Revision Note
Types of Number
You will come across vocabulary such as
Integers and natural numbers
Rational and irrational numbers
Multiples
Factors
Prime numbers
Squares, cubes and roots
Reciprocals
Knowing what each of these terms mean is essential.
What are integers and natural numbers?
Integers are whole numbers;
They can be positive, negative and zero
For example, -3, -2, -1, 0, 1, 2, 3 are all integers
Natural numbers are the positive integers
They can be thought of as counting numbers
1, 2, 3, 4, … are the natural numbers
Notice that 0 is not included
What are rational and irrational numbers?
A rational number is a number that can be written as a fraction in its simplest form
A rational number can be written in the form
where
and
are both integers, and
is not zero
All terminating decimals are rational numbers
e.g.
All recurring decimals are rational numbers
e.g.
Recurring digits are indicated by dots or bars
e.g.
e.g.
An irrational number cannot be written as a fraction
All non-terminating, non-recurring decimals are irrational numbers
(pi) is an irrational number
It has an endless amount of decimal places and there is no pattern or recurring digits
Any (simplified) fraction involving
, such as
, will also be irrational (as
in
is not an integer)
Examiner Tips and Tricks
In the calculator paper, use your calculator to your advantage!
To determine whether a number is rational or irrational, type it into your calculator and see if it can be displayed as a fraction (with integers)
Worked Example
Explain why is a rational number.
The dots indicate the first and last of the recurring digits
is a rational number as it is a recurring decimal
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