Preprint Open Access
Inder J. Taneja
The natural numbers form 1 to 11111 are written in terms of single letter "a" in two different ways. One is running-type expressions, and second is fraction-type expressions. In this work, we considered the fraction-type way. It means the numbers 1 to 11111 are written as fraction-type using only the single letter "a" . The single letter "a" can have any valure from 1 to 9, and the final result is always same. To bring these results, only basic operations, such as, addition, subtraction, multiplication and division are used. The idea of potentiation is not considered here. In another work, few numbers are written using potentiation. The running-type single letter representations can be see in author's  another work. This work is a reorganized version of author's previous work  done in 2018.