Let [tex]u=3.8\bar{3}[/tex], then [tex]10u=38.\bar{3}[/tex] and [tex]100u=383.\bar{3}[/tex]
That means [tex]90u=100u-10u=383.\bar{3}-38.\bar{3}=345[/tex].
Solving for [tex]u[/tex] gives us a fraction [tex]u=\frac{345}{90}=\boxed{\frac{23}{6}}=3.8\bar{3}[/tex].
Hope this helps.
