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# Hi! I was having trouble with this problem:

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Hi! I was having trouble with this problem:

What is 0.727272.../0.272727...? Express your answer as a common fraction in lowest terms.

Jul 25, 2020

#1
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I guess this is the easiest way:

.727272727272/.272727272727 = 2.6666666666666667     which is   2 2/3

Here is the long way

let x = .72727272....

100x = 72.72727272....

100x - x = 99x  = 72       x = 72/99     this is the numerator.....

now do similar for the denominator....then do the division to get an exact answer.....

denominator = 27/99

72/99  /  27/99   =   72/27 = 24/9= 8/3 = 2 2/3

Jul 25, 2020
edited by ElectricPavlov  Jul 25, 2020
edited by ElectricPavlov  Jul 25, 2020
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thank you :))

laureli  Jul 25, 2020
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Neither the decimal ".727272..." nor the decimal ".722222..." can be turned into a fraction.
Also to respond to CPhill's comment I'm pretty sure that he was saying that he needed the answer based on ".72 repeating" not what you assumed he meant. Also the answer you gave can be simplified to

18/25

Jul 25, 2020