Question

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

Answer 1

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   .