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# What is .4 repeating as a fraction?

Mar 5, 2018

#### Answer:

See a solution process below:

#### Explanation:

First, we can write:

$x = 0. \overline{4}$

Next, we can multiply each side by $10$ giving:

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

Then we can subtract each side of the first equation from each side of the second equation giving:

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

We can now solve for $x$ as follows:

$10 x - 1 x = \left(4 + 0. \overline{4}\right) - 0. \overline{4}$

$\left(10 - 1\right) x = 4 + 0. \overline{4} - 0. \overline{4}$

$9 x = 4 + \left(0. \overline{4} - 0. \overline{4}\right)$

$9 x = 4 + 0$

$9 x = 4$

$\frac{9 x}{\textcolor{red}{9}} = \frac{4}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} x}{\cancel{\textcolor{red}{9}}} = \frac{4}{9}$

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