Continued Fraction - Calculating Continued Fraction Representations

Calculating Continued Fraction Representations

Consider a real number r. Let i be the integer part and f the fractional part of r. Then the continued fraction representation of r is, where is the continued fraction representation of 1/f.

To calculate a continued fraction representation of a number r, write down the integer part (technically the floor) of r. Subtract this integer part from r. If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat. The procedure will halt if and only if r is rational.

Find the continued fraction for 3.245 (= )
Step Real Number Integer part Fractional part Simplified Reciprocal of Simplified
STOP
Continued fraction form for 3.245 or is

The number 3.245 can also be represented by the continued fraction expansion ; refer to Finite continued fractions below.

Read more about this topic:  Continued Fraction

Famous quotes containing the words calculating, continued and/or fraction:

    I know that the right kind of leader for the Labour Party is a kind of desiccated calculating machine.
    Aneurin Bevan (1897–1960)

    If my sons are to become the kind of men our daughters would be pleased to live among, attention to domestic details is critical. The hostilities that arise over housework...are crushing the daughters of my generation....Change takes time, but men’s continued obliviousness to home responsibilities is causing women everywhere to expire of trivialities.
    Mary Kay Blakely (20th century)

    The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.
    Charlotte Perkins Gilman (1860–1935)