# How do you find the repeating decimal 0.231 with 31 repeated as a fraction?

##### 2 Answers

Oct 20, 2016

The answer is

#### Explanation:

Starting from the second number we have an infinite sum of a convergent geometric sequence with:

So we can write the whole decimal as:

Oct 20, 2016

#### Explanation:

let

because TWO digits repeat

we have therefore:

&

Subtracting the two the repeating 31s will all cancel

we are left with