The vertex of the angle below is the center of the circle.  Find $n$ if $n\%$ of the circle is shaded.  Give your answer as a mixed fraction.

[asy]
unitsize(0.6inch);
fill((0,0)--(1,0)..(rotate(60)*(1,0))..(rotate(120)*(1,0))--cycle,gray(0.6));
draw(Circle((0,0),1));
draw((1,0)--(0,0)--(rotate(120)*(1,0)));
label("$120^\circ$",(0,0),NE);
[/asy]
There are $360$ degrees in a circle, so the portion of the circle that is shaded is \[\frac{120^\circ}{360^\circ} = \frac13 =33\frac13 \%.\]Hence, $n = \boxed{33 \frac{1}{3}}$.