Best Rational Approximation of Using Simple Continued Fractions


Authors : Amelia Lukis; Nur Erawaty; Muh. Zakir

Volume/Issue : Volume 8 - 2023, Issue 3 - March

Google Scholar : https://bit.ly/3IIfn9N

Scribd : https://bit.ly/42evQ0h

DOI : https://doi.org/10.5281/zenodo.7739281

The best rational approximation of a real number are rational numbers that are closest to the real number compared to other rational numbers with the same or smaller denominator. One of methods to find the best rational approximation is using simple continued fractions. Simple continued fraction expansion is a representation of a number that is produced through an iterative process of adding the largest integer that is less than that number, with the inverse multiplication of other numbers, with the other number is also the result of adding the largest integer that is less than it, with the inverse multiplication of another number. This research will focus on finding the best rational approximation of by using multiplication of simple continued fraction. The result obtained is best rational approximation of with 15 decimal places precision.

Keywords : Best Rational Approximation, Simple Continued Fraction, Irrational Number, Multiplication.

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