Question

How would you convert the repeating, non terminating decimal into a fraction? Explain the process as you solve the problem 0.1515

Answer 1

divide 1515 by 100 and you would get 15.15 the divide the .15 by 3 and and you will get 3.5 so the answer will be 15 3/5

Answer 2

See explanation below.

Explanation:

You have the repeating non terminating decimal x = 0.151515....

• To start converting it into a fraction, we are going to multiply both sides of the equation by 100 and we get:

100x =15.1515...

But remember that x = 0.151515... so the number 15.1515... can be written as 15 + x. We're going to write our last equation then:

100x = 15.1515...

100x = 15 + x

And now we will solve for x

100x = 15 + x

99x = 15

x = 15/99

x = 5/33

Thus, 0.1515.... can be written as 5/33 in its fraction form.