# Is -0.033333 a rational number?

Apr 9, 2015

A rational number is defined as a number that can be written as a ratio.
In the case of $- 0.033333 ,$ it is possible to write the number as a fraction.

Let $x = - 0.033333$
$100 x = -$$3.33333$
$10 x = - 0.33333$
$100 x - 10 x = -$$3.33333$-($- 0.33333$)=$3$
$90 x = 3$
$x \mathmr{and} - 0.033333$ $= \frac{3}{90} = \frac{1}{30}$

As $- 0.033333$ can be written as a fraction of $\frac{1}{30}$, it is a rational number.