# How do irrational numbers differ from rational numbers?

Mar 29, 2016

Rational numbers can be expressed as fractions, irrational numbers cannot...

#### Explanation:

Rational numbers can be expressed in the form $\frac{p}{q}$ for some integers $p$ and $q$ (with $q \ne 0$). Note that this includes integers, since for any integer $n = \frac{n}{1}$.

For example, $5$, $\frac{1}{2}$, $\frac{17}{3}$ and $- \frac{7}{2}$ are all rational numbers.

Any other Real number is called irrational. For example $\sqrt{2}$, $\pi$, $e$ are all irrational numbers.

If a number $x$ is rational, then its decimal expansion will either terminate or repeat.

For example, $\frac{213}{7} = 30.428571428571 \ldots$, which we can write as $30. \overline{428157}$.

If a number is irrational, then its decimal expansion will neither terminate nor repeat. For example,

$\pi = 3.141592653589793238462643383279502884 \ldots$