Continued fraction

Continued fraction
Fraction Frac"tion, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See {Break}.] 1. The act of breaking, or state of being broken, especially by violence. [Obs.] [1913 Webster]

Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. [1913 Webster]

2. A portion; a fragment. [1913 Webster]

Some niggard fractions of an hour. --Tennyson. [1913 Webster]

3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. [1913 Webster]

{Common fraction}, or {Vulgar fraction}, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths.

{Complex fraction}, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck.

{Compound fraction}, a fraction of a fraction; two or more fractions connected by of.

{Continued fraction}, {Decimal fraction}, {Partial fraction}, etc. See under {Continued}, {Decimal}, {Partial}, etc.

{Improper fraction}, a fraction in which the numerator is greater than the denominator.

{Proper fraction}, a fraction in which the numerator is less than the denominator. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • Continued fraction — Continued Con*tin ued, p. p. & a. Having extension of time, space, order of events, exertion of energy, etc.; extended; protracted; uninterrupted; also, resumed after interruption; extending through a succession of issues, session, etc.; as, a… …   The Collaborative International Dictionary of English

  • continued fraction — n. a fraction whose denominator consists of a whole number plus a fraction whose denominator consists of a whole number plus a fraction, and so forth …   English World dictionary

  • Continued fraction — Finite continued fraction, where a0 is an integer, any other ai are positive integers, and n is a non negative integer. In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the… …   Wikipedia

  • continued fraction — Math. a fraction whose denominator contains a fraction whose denominator contains a fraction, and so on. [1860 65] * * * ▪ mathematics       expression of a number as the sum of an integer and a quotient, the denominator of which is the sum of an …   Universalium

  • continued fraction — fraction whose denominator is a fraction whose denominator is a fraction and so on …   English contemporary dictionary

  • Continued fraction of Gauss — In complex analysis, the continued fraction of Gauss is a particular continued fraction derived from the hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several… …   Wikipedia

  • Continued fraction factorization — In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties.… …   Wikipedia

  • continued fraction — /kənˌtɪnjud ˈfrækʃən/ (say kuhn.tinyoohd frakshuhn) noun Mathematics a fraction whose denominator contains a fraction whose denominator contains a fraction, and so on. Also, recurring fraction …  

  • 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 • Hypernyms: ↑fraction …   Useful english dictionary

  • continued fraction — noun Date: 1811 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 …   New Collegiate Dictionary

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