jmc

We can express the decimal as a geometric series, with first term $.283$, and common ratio $.001$.

Let S denote the sum of this infinite geometric series:

$S=.283+.000283+\dots$

Then,

$1000S=283.283283283\dots$

Thus,

$999S=283$

and

$S=\frac{283}{999}$

Thus, $3.283283\cdots =3+\frac{283}{999}=\boxed{\frac{3280}{999}}$