Convert 5.764764764 … to a rational expression in the form of a over b, where b ≠ 0

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22-08-2016
Mathematics

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Convert 5.764764764 … to a rational expression in the form of a over b, where b ≠ 0

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AL2006 AL2006 · Answer 1 · 2016-08-22T18:48:52+02:00

I just learned a short time ago how to convert a repeating decimal to a fraction.

-- Take the repeating part of the decimal. In this one, it's '764' .

-- Make a fraction out of it by writing it over the same number of 9s.

   The fraction here is 764/999 .

-- Simplify it if possible and if you feel like it.

   764/999 can't be simplified. (I think.)

So the rational expressions for this decimal are

   (5 and 764/999)   or   5759/999   .