# A Computational Criterion for the Irrationality of Some Real Numbers

Document Type : Research Paper

Author

Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran

Abstract

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.

Keywords