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.

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