Question

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

Answer 1

let x = .151515...
multiply by 100, (note there were 2 digits repeating, and there are 2 zeros in 100)
100x = 15.151515...
subtract the two equations:
99x = 15
x = 15/99 = 5/33 , check with a calculator.

Suppose you have some initial decimals that don't repeat,
e.g.
.34123123123...
let x = .34123123123...
three digits repeat, so I multiply by 1000
1000x = 341.23123123...
subtract them, make sure to line up the decimals and notice the 123123... match up
999x = 340.89
x = 340.89/999 , but we don't want decimals in our fraction
= 34089/99900

Answer 2

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