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Question
Hello:

How is a repeating decimal like 0.272727... changed to the fraction 3/11 by using a geometric series?

Let x = 0.2727...
The repeating digits are 27.

Multiply x by 100 so there is one repeat to the left of the decimal point
100x = 27.2727...

subtract the first equation from the second equation
100x = 27.2727...
-x = -0.2727...
---------------
99x = 27

x = 27/99 = 3/11

I just realized that I didn't use a geometric series to answer the question. I've never tried it that way, but if I find out how, I'll revise this.
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#### Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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