Irrational Number: GCSE Maths Definition

What is an irrational number?

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

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.

So an irrational number is any number that cannot be written as a fraction in that form.

What are some common irrational numbers?

The most famous irrational number you will come across in GCSE Maths is π  (pi).

Surds are another common type of irrational number that you will see in GCSE Maths. Any number of the form , where is a positive integer but is not a square number, is irrational. So , and are all irrational numbers. But is not, because which is rational.

What about the decimal form of an irrational number?

The decimal form of an irrational number does not terminate (end) and is not recurring (repeating forever in a pattern). For example:

The decimal versions of those numbers never end, and there are no patterns of repeating digits in them.

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.

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