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

There are 5 steps to convert a repeating decimal to fraction. And these are the following steps:
Step 1: Let x be the repeating decimal you are converting to a fraction. [x = 0.555555555]
Step 2: Look for the repeating digit(s). [the repeating digit is 5]
Step 3: Place the repeating digit(s) to the left of the decimal point [move the decimal point 1 place to the right, moving is the same as multiplying the decimal number by 10 so it will become, 10x = 5.555555555]
Step 4: Place the repeating digit(s) to the right of the decimal point [x = 0.5555555555]
Step 5: Subtract the left sides of the two equations.Then, deduct the right sides of the two equations.[Your two equations are:
10x = 5.555555555
x = 0.5555555555
10x - x = 5.555555555 − 0.555555555555
9x = 5
x = 5/9]