Explain step by step how to make a repeating decimal become into a fraction form?

Suppose we have the repeat decimal 0.123232323.... or 0.123 with a line over the repeated part (check the diagram)
- The first thing we need to do is identify the part of the decimal that repeats, 23 in  our case.
- Second, we are going to assign a variable to our original decimal:      .
- Third, we are going to multiply both sides by a power of ten whose denominator will be the number of repeating digits. We know that we have 2 repeating digits (23), so we are going to multiply both sides by , and  is just 100; therefore we get:
 

- fourth, subtract our original equation from the second step from the one from above:

Now we can cancel the repeated decimals to get:



- Last but not least multiply both numerator and denominator by a power of ten equals to the decimal digits in the numerator:


We now know how to convert a repeating decimal to a fraction.