Question

What is `0.8959595...` as a fraction ?

Answer 1

`0.8bar(95) = 887/990`

Explanation:

Given:

`0.8bar(95)`

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

`(1000-10)*0.8bar(95) = 895.bar(95) - 8.bar(95) = 887`

Then divide both ends by `(1000-10)` to find:

`0.8bar(95) = 887/(1000-10) = 887/990`

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