A continued fraction is a way to represent a number through a sequence of fractions. It starts with an integer part and continues with a series of fractions, where each fraction has an integer in the numerator and another continued fraction in the denominator. This representation can provide more precise approximations of irrational numbers, such as π or e. Continued fractions can be finite or infinite. Finite continued fractions represent rational numbers, while infinite continued fractions often represent irrational numbers. They are useful in various fields, including number theory and approximation theory, as they can reveal properties of numbers and help in finding their best rational approximations.