How do you Use an infinite geometric series to express a repeating decimal as a fraction?
1 Answer
Sep 19, 2014
Let us find a fraction for
by splitting it into
by rewriting each term as a fraction,
by rewriting a little further,
The series above is a geometric series with
Hence, the sum is
#0.121212...=a/{1-r}={12/100}/{1-1/100}={12/100}/{99/100}=12/99=4/33#
