The continued fraction representation of a number is a sum of two terms. The first is the number's integer part. The second is recursively defined as the reciprocal of the continued fraction form of the reciprocal of the original number's fractional part. Rational numbers can be represented by finite continued fractions while irrationals require infinitely deep representations. Wolfram|Alpha can be used to convert between and utilize these representations. It also possesses knowledge about symbolic continued fractions as well as related theorems and algorithms.
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