Continued Fractions - Cornell University

Every rational number has a simple continued fraction expansion which is nite and every nite simple continued fraction expansion is a rational number. Proof. Suppose we start with a rational number, then Euclid’s algorithm terminates in nitely many steps. This is because the successive reminders are strictly decreasing as they have to

  Number, Fractions, Continued, Rational, Rational numbers, Continued fractions