$\text{a)}$  

$0,666\dots =x\text{|}\cdot 10$  

$6,666\dots =10x$  

$6+\underset{x}{\underbrace{0,666\dots }}=10x$  

$6+x=10x$  

$6=9x\mid :9$  

$x=\frac{6}{9}=\frac{2}{3}$  

Odp.  $0,\left(6\right)=\frac{2}{3}.$  

$\text{b)}$  

$0,363636\dots =x\text{|}\cdot 100$  

$36,363636\dots =100x$