How would you convert the repeating, nonterminating decimal to a fraction?

Please explain the process as you solve the problem, \(0.\overline{15}\).

Please provide the answer in words and numbers. Give 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

Answered by KMK32 | 2024-06-10

To convert the repeating decimal 0. 15 into a fraction, assign it to a variable, multiply to eliminate the repeating part, set up and simplify the resulting equation to arrive at 33 5 ​ .
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Answered by KMK32 | 2024-09-30