Repetitiously

Here's an example that might help:

If $x=0.1\dot{6}$, then $10x=1.\dot{6}$

$1.\dot{6}$ is also $x+1.5$

So $$\eqalign{10x&=x+1.5 \cr \Rightarrow 9x&=1.5 \cr \Rightarrow 18x&=3 \cr \Rightarrow x&=\frac3{18} = \frac16}$$