How you would convert the repeating, nonterminating decimal to a fraction? explain the process as you solve the problem, 0.
give me the answer in words and numbers! give me an explanation for each numerical step.

Okay, here we go.

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