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Homework Statement
Express the repeating decimal as a series, and find the rational number that it represents1) 3.2[itex]\overline{394}[/itex]
Homework Equations
Geometric Series (a/1-r)The Attempt at a Solution
I tried putting the value into a series by having n=1 as it goes to infinityƩ3.2 + 394(0.0001)n
but I have a feeling that is wrong. Is there anyway to just isolate the 0.0394 as the repeating value?
I also tried using (3.2 + 394) as "a", and (0.0001) as "r"
putting this into the geometric series formula to find the rational number I got
((16/5) +394)/(1-0.0001) which came out to be 1986/0.9999
The Correct answer for the rational expression is 16,181/4,995
but I don't know how to get there. I have a feeling that I chose my "a" and "r" incorrectly