Say you have the repeating decimal 0.333... repeating.
First let x equal the repeating decimal:
x=0.333...
we can now multiply this by 10 to get
10x=3.333...
now I can write 10x-x as follows
10x-x=3.333...-0.333...
Therefore
9x=3 => x=1/3
1/3 = 0.333...
You basically want to try arrange it so you eliminate the repeating decimal which enables you to write x as a fraction.
