jmc

Note that 111 and 9999 have a common factor of 3. Also, 33 and 3333 have a common factor of 33. We get $$\begin{array}{rl}\frac{\text{cancelto}37111}{\text{cancelto}33339999}\cdot 33& =\frac{37}{\text{cancelto}1013333}\cdot \text{cancelto}133\\ & =\boxed{\frac{37}{101}}.\end{array}$$