Question

1. How do you convert the repeating, nonterminating decimal 0.1515... to a fraction?

Explain the process as you solve the problem.

Answer 1

`(5)/(33)`

Explanation:

Create 2 equations with the repeating decimal after the decimal point, then subtract them to eliminate the repeating decimal

let x = 0.1515... → (1) ( multiply both sides by 100 )

100x = 15.1515... → (2)

Subtract (1) from (2)

99x = 15 ( eliminating the repeating decimal )

divide both sides by 99

x =
`(15)/(99)` =
`(5)/(33)`

Answer 2

15/99.

Explanation:

0.1515.. * 100 = 15.1515....

0.1515.. * 1 = 0.1515.....

Subtracting:

0.1515... * 99 = 15

Answer is 15/99.