# How do you express .33 as a fraction in simplest form?

Sep 14, 2016

$\frac{33}{100}$

Sep 14, 2016

As you wrote the question $\frac{33}{100}$

If you meant $0.333333 . . \to 0.33 \overline{3} \text{ }$ then $\text{ } \frac{1}{3}$

#### Explanation:

It all depends on what you mean by $0.33$

If you meant it to be exactly as written then we have

$\frac{3}{10} + \frac{3}{100}$

Write as $\left(\frac{3}{10} \times 1\right) + \frac{3}{100}$

But 1 may be written as $\frac{10}{10}$

$\left(\frac{3}{10} \times \frac{10}{10}\right) + \frac{3}{100}$

$\frac{30}{100} + \frac{3}{100} = \frac{33}{100}$

$\textcolor{red}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

If you meant what you wrote to mean $0.33 \leftarrow$ 3 going on for ever

$0.333333333 \ldots . .$ written as $0.33 \overline{3}$

$\textcolor{b r o w n}{\text{Then this is very different:}}$

Let $x = 0.33 \overline{3}$

thus $10 x = 3.33 \overline{3}$

$10 x - x = 3$

$9 x = 3$

$x = \frac{3}{9} = \frac{1}{3}$