Do the inherent limitations of classical fractions keep you up at night? Do you wring your hands in frustration at the blandness that is the denominator? If you answered yes to both of these, one of these, or even neither of these, you'll be glad to know that continued fractions have you covered. In this class, we'll explore some surprising results about continued fractions and learn about their application to rounding, approximation, tax fraud, and even Pell's equation. As a bonus, check out the cool example below! $$ \pi=3+\frac{1^2}{6+ \frac{3^2}{6+ \frac{5^2}{6+\dots }}} $$