MATC Mathematics Club
Lecture #95
Madison Area Technical College
Madison, Wisconsin
Professor Elgin Johnston, Iowa State U
"Repeating Repeating Decimals"
Previous Lectures: ("Mass Points: Geometry by Physics"), ("Wine bottles and Pizza sharing"),
("Choosing Your Ideal Companion and Other Probabilistic Surprises")
Abstract: Calculate the decimal expressions for 1/7 ; 2/7 ; 3/7 ; . . . ; 6/7 to see 1/7 = 0.142857142857 . . . 3/7 = 0.428571428571. . .2/7 = 0.285714285714. . . 6/7 = 0.857142857142 . . .4/7 = 0.571428571428 . . . 5/7 = 0.714285714285 . . . Note that repeating block cycles as we read down the list of fractions. Does this happen with other fractions? When? Is there some interesting structure to other decimal representations for fractions? 1
Biography: Elgin Johnston <http://www.math.iastate.edu/ehjohnst/> earned his PhD in 1977 from the University of Illinois at Urbana, where he worked in approximation theory and complex analysis. He is currently Associate Chair of the Mathematics Department at Iowa State, Problem Section Editor for Mathematics Magazine, and Chair of the Committee on American Mathematics Competitions. His areas of active interest include problem solving, complex analysis, and working with mathematically gifted pre-college students. His leisure activities include biking, brewing beer, playing guitar, and reading history, mysteries, and science fiction
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