Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
Welcome to MSE! Do you have any thoughts or tried anything on the problem? Regards – Amzoti Apr 22 '13 at 4:27

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.