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Rational Number: GCSE Maths Definition

Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Published

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2 minutes

Contents

  1. 1. What is a rational number?
  2. 2. How can I tell if a decimal number is a rational number?
  3. 3. GCSE Maths Revision Resources to Ace Your Exams

What is a rational number?

A rational number is a number that can be written as a fraction, with an integer on the top of the fraction and an integer on the bottom of the fraction. For example, 3 over 16, 2 over 7 and 1973 over 877 are all rational numbers.

Integers are also rational numbers. Remember that an integer can always be written as a fraction over 1. For example, 5 equals 5 over 1.

The same definition also holds for negative numbers. For example, negative 5 over 8 equals fraction numerator negative 5 over denominator 8 end fraction equals fraction numerator 5 over denominator negative 8 end fraction is a rational number, as is negative 3 equals fraction numerator negative 3 over denominator 1 end fraction equals fraction numerator 3 over denominator negative 1 end fraction.

If a number is not rational, then it is irrational.

How can I tell if a decimal number is a rational number?

For a rational number, the decimal form of the number either terminates (ends), or is recurring (repeats forever in a pattern). For example:

  • 3 over 16 equals 0.1875

    • the decimal version ends at the 5

  • 2 over 7 equals 0.2 with dot on top 8571 4 with dot on top equals equals 0.285714285714285714285714...

    • the digits '285714' keep repeating forever

GCSE Maths Revision Resources to Ace Your Exams

To see more on rational and irrational numbers, read our revision notes on Types of Number. You can also have a go at our related exam questions. For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. And don’t forget to check out the past papers for more general exam revision.

Explore GCSE Maths revision resources

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Reviewer
Roger B

Author: Roger B

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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