Some generalizations and limit theorems on cancellable numbers

Abstract

A cancellable number (CN) is a fraction in which a decimal digit can be removed (“canceled”) in the numerator and denominator without changing the value of the number; examples include $\frac{64}{16}$ where the 6 can be canceled and $\frac{98}{49}$ where the 9 can be canceled. We present a few limit theorems and provide several generalizations.