# Express

Question:

Express $0 . \overline{4}$ as a rational number in simplest form.

Solution:

Let $x$ be $0 . \overline{4}$

$x=0 . \overline{4}$

Multiplying both sides by 10, we get

$10 x=4 . \overline{4}$

Subtracting (1) from (2), we get

$10 x-x=4 . \overline{4}-0 . \overline{4}$

$\Rightarrow 9 x=4$

$\Rightarrow x=\frac{4}{9}$

Thus, simplest form of $0 . \overline{4}$ as a rational number is $\frac{4}{9}$.