Convert the repeating decimal $3.283283283\ldots$ to an improper fraction.
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, $3.283283\dots = 3 + \frac{283}{999} = \boxed{\frac{3280}{999}}$