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Prove that decimal representation is unique iff the number has no terminating expansion. Prove also that any terminating expansion also has a nonterminating expansion. How are these nonterminating expansions constructed?

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Welcome to MSE! Do you have any thoughts or tried anything on the problem? Regards –  Amzoti Apr 22 '13 at 4:27
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Hint: the important idea is that $1=0.9999\ldots $ This will let you solve the second and third. The first depends on what you have to work with, but the idea is that aside from this any two expansions are a ways apart.

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