How to express the following number as a ratio of integers:
$10.1\overline {35}$
where 35 repeats infinetly. so:
$10.135353535353535353535353535\cdots$
Basically I did this so far
$\frac {101}{10} + (.35) *$ geometric infinite series $\left(\frac 1{10}\right)^n$
But this isn't right. What am I doing wrong with my infinite series? I want to make it correct so I can use the sum formula.
The answer is: $\frac {5017}{495}$
But I'm not sure how to get that answer.
$\endgroup$ 71 Answer
$\begingroup$Let say $x=10.1353535...$.
Then $1000x=10135.3535...$ and $10x=101.3535...$
Subtracting these both equations gives
$990x=10034$ which after simplifying gives
$x=10.1353535..=5017/495$
$\endgroup$ 1
