Irrational number

Definition

An irrational number cannot be written as a fraction a/b of two integers. Its decimal form never ends and never repeats. Square roots of numbers that are not perfect squares, such as √2 and √7, and π are irrational.

Worked example

√7 ≈ 2.6457… is irrational, but √9 = 3 is rational.

0.333… is rational because it equals 1/3, even though the decimal goes on forever: it repeats.

Where it appears in the exam

Irrational number is part of the numbers section of CAPS Grade 9 Mathematics and appears in school tests and the end-of-year exam.

Step-by-step method

1. Check whether the number can be written as a fraction of integers.
2. For a square root, check whether the number under the root is a perfect square.
3. For a decimal, check whether it ends or repeats; if it does neither, it is irrational.

Common mistake

Thinking every never-ending decimal is irrational; repeating decimals are rational.

Related numbers terms

• Scientific notation

Frequently asked questions

What does irrational number mean in Grade 9 Maths?

An irrational number cannot be written as a fraction a/b of two integers. Its decimal form never ends and never repeats. Square roots of numbers that are not perfect squares, such as √2 and √7, and π are irrational.

When do you learn about irrational number?

Irrational number is taught in the numbers section of CAPS Grade 9 Mathematics and is used again in Grades 10 to 12.

How do I practise questions involving irrational number?

Snap a question that uses irrational number into Snap&Learn with your grade set to Grade 9, or work through the Grade 9 topic guide and practice papers.