# 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

## Examples of continued fraction in a Sentence

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

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'continued fraction.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

First Known Use

1811, in the meaning defined above

Time Traveler
The first known use of continued fraction was in 1811

## Dictionary Entries Near continued fraction

continued fraction

## Cite this Entry

“Continued fraction.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/continued%20fraction. Accessed 18 Jul. 2024.

## 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

## More from Merriam-Webster on continued fraction

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