With simpler decimals, this is a bit easier so I'll explain that first to make sure you get the basic idea.
Let's say you had a decimal for .75 and wanted to create the fraction mathematically. To do this you would:
First divide the decimal by 1 so .75/1 Then multiply be a multiple of 10 that eliminates the decimal so in this case 100 so you now have 75/100 When you simplify that fraction by dividing by 25, you of course get 3/4
Now on to your more complicated question:
Let's assign a variable to your repeating decimal so:
x=.1515151515
Now, let's identify the repeating digits, here they are .15
Move one set of the repeating digits in front of the decimal so now we get:
100x=15.1515151515
Now you have two equations, they are:
x=.1515151515 100x=15.1515151515
Combine the equations into one equation:
100x-x=15.1515151515-.1515151515 99x=15 15/99 simplify and you get 5/33
