Convergent (continued fraction)
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Convergent (continued fraction)

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A convergent is one of a sequence of values obtained by evaluating successive truncations of a continued fraction. The nth convergent is also known as the nth approximant of a continued fraction.Every real number can be expressed as a regular continued fraction in canonical form. Each convergent of that continued fraction is in a sense the best possible rational approximation to that real number, for a given number of digits. Such a convergent is usually about as accurate as a finite decimal expansion having as many digits as the total number of digits in the nth numerator and nth denominator....