A Computational Criterion for the Irrationality of Some Real Numbers

06/30/2020

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by   Peyman Nasehpour, Ph.D., et al.

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In this paper, we compute the asymptotic average of the decimals of some real numbers. With the help of this computation, we prove that if a real number cannot be represented as a finite decimal and the asymptotic average of its decimals is zero, then it is irrational. We also show that the asymptotic average of the decimals of simply normal numbers is 9/2.