A Criterion for the Irrationality of Some Real Numbers

In this paper, we calculate the asymptotic average of the decimals of some real numbers. For example, we show that the asymptotic average of the decimals of simply normal numbers is $9/2$. We also prove that if a real number $r$ cannot be represented as a finite decimal and the asymptotic average of its decimals is zero, then $r$ is irrational.