Answer :

[tex]x=0.666...\\ 10x=6.666...\\ 10x-x=6.666...-0.666...\\ 9x=6\\ x=\frac{6}{9}=\frac{2}{3}[/tex]
The answer quite simply is: 2/3.

1/3=0.3333333333.......
2/3=0.6666666666.......
3/3=2/3+1/3=0.9999999999.......