Which is bigger, 0.9999999…. or 1?

One way to argue that 0.99999… is equal to 1 is the following:


Multiply the above equation by 3,


Is the above convincing?

If you are still not convinced, we can let x=0.99999…

Then, 10x=9.99999…



Hence, x=1.

Grade 4 Decimals & Fractions (Kumon Math Workbooks)

There are also more advanced methods of proving 0.999…=1, listed here on Wikipedia. (http://en.wikipedia.org/wiki/0.999…) Some of the techniques include Infinite series and sequences, Dedekind cuts, and Cauchy sequences.

Author: mathtuition88


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