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.
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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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