Question 4
A recurring decimal is a decimal representation of a number whose digits are periodic in nature, meaning that, after some places, the same sequence of digits repeats continuously. For example, $\frac{1234}{9999}=0.12341234\ldots=0.\overline{1234}$. It is known that the recurring decimal of $\frac1{17}$ is 16 digits long. What is the sum of all the digits of the recurring decimal of $\frac1{17}$?