Answer :

Well Calculate the sum of 1/2 + 3*sum(n=2 to infinity) [ 1/10^n ] = 8/15 The answer would be 8/15.I hope this answer is right! 
[tex]x=0.5\overline{3}\\ 10x=5.\overline{3}\\ 100x=53.\overline{3}\\ 100x-10x=53.\overline{3}-5.\overline{3}\\ 90x=48\\ x=\dfrac{48}{90}=\dfrac{8}{15}[/tex]