## Repeating Decimal Expansions |

**Professor Emeritus Karl Zimmermann**

Union College

April 19, 2016

5:00pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 4:45pm

It is well known that the decimal expansion of a rational number is either purely repeating or eventually repeating. In other words, there is some point in the expansion at which the rest is made up of the same finite string of digits repeated over and over again. In this talk, we’ll begin by using long division to explain why this repetition must occur. We’ll then call on a theorem from elementary number theory* to determine the length of the repeating strings when the denominator of the rational number is prime. Finally, we’ll state the corresponding results for non-prime denominators. * Number Theory is NOT a prerequisite for this talk!!

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Tue Oct 23 05:11:54 EDT 2018 |