# Two Irrational Numbers That Give the Last Non-Zero Digits of $n!$ and $n^n$

## TL;DR

This paper constructs irrational numbers from sequences of last non-zero digits of factorials and powers, revealing new properties of these digit patterns and their relation to irrationality.

## Contribution

It introduces a novel approach to generating irrational numbers using last non-zero digits of factorials and powers, connecting digit patterns to irrationality.

## Key findings

- The constructed numbers are proven to be irrational.
- Patterns in last non-zero digits influence the irrationality.
- New connections between digit sequences and number theory are established.

## Abstract

If we form a decimal where the nth digit is the last non-zero digit of $n!$ (likewise, the last non-zero digit of $n^n$), we obtain an irrational number