# How can I tell a rational and irrational number apart?

May 27, 2015

Well, an irrational number such as $\pi$ has an $\infty$ number of digits after the point and they do not present a recognizable pattern.
A rational number (the result of dividing two integer numbers) either stops after some digits or has $\infty$ digits but following a pattern (repetitions for example).
Examples:
Rationals:
$5 = \frac{5}{1}$
$\frac{1}{2} = 0.5$
$\frac{2}{3} = 0.6666666666 \ldots .$ always the same number after the point!
$\frac{6}{11} = 0.5454545454 \ldots$ always the same pattern of repeating 54!

An irrational number doesn't follow a pattern after the point, the decimal goes on forever without repeating. Remember that you cannot write your irrational as a fraction of two integers.

You can have "important" irrational numbers as $\pi$ oe $e$ or the result of square roots as $\sqrt{2} = 1.414213562 \ldots .$.