Quandaries and Queries


If k=.9repeating, and 10k=9.9repeating then 10k-k=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating

It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify?




The ideas behind the answer to this question are fundamental in a great deal of mathematics. A process is seen as infinite if it continues indefinitely without stopping.This concept of a process that repeats indefinitely is what I see when I read 0.999... Here I see the process of continually writing nines on the end of the string, and repeating without stopping. In mathematics however we also talk about the object that results from the completion of the process. In this example the object that results is the number 1. You will learn more about this idea when you study calculus.



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