Question 55
For each $x \in \mathbb{R}$, let $\{x\}$ be the fractional part of $x$ in its decimal representation. For instance, $\{3.4\} = 3.4 - 3 = 0.4$, $\{2\} = 0$, and $\{-2.7\} = -2.7 - (-3) = 0.3$. Find the sum of all real numbers $x$ for which $\{x\} = \frac{1}{5} x$.