Convert the repeating decimal $3.283283283\ldots$ to an improper fraction.
To convert a repeating decimal to a fraction, I need to find a way to eliminate the decimal part by multiplying both sides of an equation by a power of 10. First, I will let $x = 3.283283283\ldots$ and write it as an equation. This gives me $1000x = 3283.283283\ldots$. Now, I can subtract the original equation from this one to eliminate the repeating part. This gives me $1000x - x = 3283.283283\ldots - 3.283283283\ldots$. Simplifying, I get $999x = 3280$. Dividing both sides by 999, I get $x = \frac{3280}{999}$. This is the improper fraction that represents the repeating decimal. 