# How do you convert 3.3 (3 repeating) as a fraction?

Jun 25, 2018

See a solution process below:

#### Explanation:

First, we can write:

$x = 3. \overline{3}$

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

$10 x = 33. \overline{3}$

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

$10 x - x = 33. \overline{3} - 3. \overline{3}$

We can now solve for $x$ as follows:

$10 x - 1 x = \left(33 + 0. \overline{3}\right) - \left(3 + 0. \overline{3}\right)$

$\left(10 - 1\right) x = 33 + 0. \overline{3} - 3 - 0. \overline{3}$

$9 x = \left(33 - 3\right) + \left(0. \overline{3} - 0. \overline{3}\right)$

$9 x = 30 + 0$

$9 x = 30$

$\frac{9 x}{\textcolor{red}{9}} = \frac{30}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} x}{\cancel{\textcolor{red}{9}}} = \frac{3 \times 10}{\textcolor{red}{3 \times 3}}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 10}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{3}}} \times 3}}$

$x = \frac{10}{3}$