SOLUTION: I have a homework problem that I unfortunately do not understand how to set up to get the answer. My question is to "express the given repeating decimal as a quotient of integers.

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Question 571505: I have a homework problem that I unfortunately do not understand how to set up to get the answer. My question is to "express the given repeating decimal as a quotient of integers. If possible reduce to lowest terms." It is the repeating decimal 0.71...
Found 2 solutions by reviewermath, josmiceli:
Answer by reviewermath(518) About Me  (Show Source):
You can put this solution on YOUR website!
0.717171... = 71%2F99
Solution:
Let x = 0.717171... multiply both sides by 100 because 2 digits are repeating
100x = 71.717171...
Subtract the first equation from the second equation, the result is
99x = 71
x = 71/99
Answer: 71%2F99

Answer by josmiceli(9671) About Me  (Show Source):
You can put this solution on YOUR website!
The number is +n+ = .717171 . . .
One you learn this, you will never forget it!
+100n+ = 71.717171 . . .
+n+ = .717171 . . .
+100n+-+n+=+71+
+99n+=+71+
+n+=+71%2F99+
Looks good on my calculator