# What is 0.8959595... as a fraction ?

Jan 9, 2017

$0.8 \overline{95} = \frac{887}{990}$

#### Explanation:

Given:

$0.8 \overline{95}$

First multiply by $10 \left(100 - 1\right) = 1000 - 10$ to get an integer. The first multiplier $10$ is to shift the repeating pattern to just after the decimal point. Then $\left(100 - 1\right)$ shifts the number $2$ places to the left and subtracts the original value to cancel out the repeating tail:

$\left(1000 - 10\right) \cdot 0.8 \overline{95} = 895. \overline{95} - 8. \overline{95} = 887$

Then divide both ends by $\left(1000 - 10\right)$ to find:

$0.8 \overline{95} = \frac{887}{1000 - 10} = \frac{887}{990}$

$887$ and $990$ have no common factor larger than $1$, so this fraction is in simplest form.