How do i turn reapeating decimals into fractions?

Easy example that shows :

Let .

Then .

So , or , and so .

The basic idea is to find the period of the repeating decimal, move the digits belonging to one period over to the left of the decimal point by multiplying by , then subtract the original repeating decimal from this new number, and finally divide by .

A slightly more complicated example:

Let .

Then .

Then , or