Question

How you would convert the repeating, nonterminating decimal to a fraction? Please EXPLAIN the process as you solve the problem, 0.1515...

Please give me the answer in Words AND Numbers! Give me an explanation for each numerical step.

Answer 1

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