Rational and Irrational Numbers

A rational number can be written as a fraction of two integers, while an irrational number cannot, because its decimal never ends and never repeats. In NSW Year 8 maths you sort numbers such as \(-2.5\), \(0.\dot{6}\), \(\sqrt{5}\) and \(\pi\) into these two groups (NESA outcome MA4‑FRC‑C‑01).

You will write terminating and recurring decimals as fractions to show they are rational, decide which square roots are irrational, place \(\sqrt{2}\) on a number line and order values like \(\pi\), \(\frac{22}{7}\) and \(\sqrt{10}\). You will also find a rational number between two roots and keep answers exact until the last step. The circumference of a drink coaster and the edging around a square garden bed are irrational lengths. It is part of Year 8 Working with Numbers.