# How do you convert .8333 as a fraction?

Nov 22, 2015

$\frac{8333}{10000}$

#### Explanation:

It really depends how precise they want you to be. In the question there are 4 significant figures, so it's in the ten thousandths place.

However if we were to round we could get a more accessible number.

$\frac{8}{10}$ = $\frac{4}{5}$

It really just depends if you can round, if not then set it over the proper denominator (tenths, hundredths, thousandths, etc) and simplify as usual.

Hope that helps!

Nov 22, 2015

Assumption: The given value in the question is a repeating decimal.

$.833 \overline{3} = \frac{5}{6}$

#### Explanation:

The format of the proposed question implies that this is a repeating decimal. If so then the approach would be:

Let $x = 0.83 \overline{3} \text{ }$
Where the bar above the last 3 means that the 3 goes on repeating for ever. $\textcolor{p u r p \le}{\text{You can use a dot or a bar for this.}}$

Then $10 x = 8.33 \overline{3}$

So $10 x - x = 7.5$

$x \left(10 - 1\right) = 7.5$

$x = \frac{7.5}{9}$

To get rid of the decimal

$x = \frac{7.5}{9} \times 1$

But write 1 as $\frac{2}{2}$ giving

$x = \frac{7.5}{9} \times \frac{2}{2} = \frac{7.5 \times 2}{9 \times 2}$

$x = \frac{15}{18} = \frac{5}{6}$