Irrational Number Definition: a plain-English explanation of what the term means, why it matters in math, and how it is used, followed by worked examples and practice questions so the definition turns into something you can apply.
Math Dictionary / Irrational Number
Irrational Number
An irrational number cannot be written as a fraction of two integers.
Number SystemGrade 8Algebra 1SATACT
What it means
Its decimal form does not end and does not repeat in a pattern.
Also called: non-repeating decimal
Examples
| sqrt(2) is irrational |
| pi is irrational |
| 0.121121112… can be irrational if it never repeats |
Common mistake
A long decimal is not automatically irrational. Repeating decimals are rational.
Try one
Question: Is sqrt(49) irrational?
Show answer
No. sqrt(49) = 7, and 7 is rational.