Let $$x = 0.555\cdots$$  Multiply by $$10$$ , which means move the decimal point one place to the right: $$10x = 5.555\cdots$$.  $$x$$ and $$10x$$ have exactly the same decimal part, so if we subtract, it will disappear: $$10x - x = 5.555\cdots - 0.555\cdots$$.  Simplify:~ $$9x = 5$$，$x=\dfrac{5}{9}$  So there\textquotesingle s our answer : $$0.555\cdots=$$$\dfrac{5}{9}$ 
Express $$0.\dot{5}$$ as a fraction . ． 
Options:
[A] $\dfrac{111}{200}$ 
[B] $\dfrac{11}{20}$ 
[C] $\dfrac{5}{9}$ 
[D] $\dfrac{2}{3}$ 