# How do you simplify and make the fraction 4/33 into a decimal?

Oct 4, 2015

You can long divide $4$ by $33$ and observe the repeating remainder, or simply notice that $\frac{4}{33} = \frac{12}{99} = 0.121212 \ldots = 0. \dot{1} \dot{2}$

#### Explanation:

First note that $4$ and $33$ have no common factor greater than $1$, so $\frac{4}{33}$ is already in simplest form.

When we start to long divide $4$ by $33$ it only takes a couple of digits to get back to the number we first started with...

So we get a repeating decimal expansion:

$\frac{4}{33} = 0.121212 \ldots = 0. \dot{1} \dot{2}$

Alternatively, note that $\frac{4}{33} = \frac{3 \cdot 4}{3 \cdot 33} = \frac{12}{99} = 0. \dot{1} \dot{2}$