# Two Irrational Numbers from the Last Nonzero Digits of $$n!$$ and $$n^n$$

by Gregory Dresden

This article originally appeared in:
Mathematics Magazine
October, 2001

Subject classification(s): Algebra and Number Theory | Number Theory | Irrational Numbers
Applicable Course(s): 4.3 Number Theory

The author considers two infinite decimals, where the $$n$$th digit is the last non-zero digit of $$n!$$, creating the number $$F$$, and using $$n^n$$, creating the number $$P$$. The author shows that both $$F$$ and $$P$$ are irrational.

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Capsule Course Topic(s):
Number Theory | Irrationality
Number Theory | Numbers With Special Forms or Properties, Base Representation and Decimal Expansion