continued fraction

noun

: a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on

Example Sentences

Recent Examples on the Web

Like its transcendental cousin π, e can be represented in countless ways — as the sum of infinite series, an infinite product, a limit of infinite sequences, an amazingly regular continued fraction, and so on. —Quanta Magazine, 24 Nov. 2021

Continued fractions are approximations; as the height of the tower of numerators and denominators grows, the continued fraction approximation gets closer to the irrational number being approximated. —Evelyn Lamb, Popular Mechanics, 23 Feb. 2021

The insight of the continued fraction approach to solving Pell’s equation is that when x and y are large, a difference of 1 is relatively small. —Evelyn Lamb, Popular Mechanics, 23 Feb. 2021

That’s step one in converting to a continued fraction. —Popular Mechanics, 21 Feb. 2021

Word History

First Known Use

1811, in the meaning defined above

Kids Definition

continued fraction

noun

: a fraction whose numerator is a whole number and whose denominator is a whole number plus a fraction whose numerator is a whole number and whose denominator is a whole number plus a fraction and so on