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A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction, which may itself be a simple or a continued fraction. If this iteration terminates with a simple fraction, the result is a finite continued fraction; if it continues indefinitely, the result is an infinite continued fraction. The special case in which all numerators are equal to one, and all denominators are positive integers, is referred to as a simple continued fraction. Any positive rational number can be expressed as a finite simple continued fraction, and any positive irrational number can be expressed as an infinite simple continued fraction.
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