0
$\begingroup$

Possible Duplicate:
How can I prove that all rational numbers are either terminally real or repeating real numbers?

How can i prove that every terminating real number is rational and every repeating real number is a rational number?

I was given a hint: Prove that $\{0.1^i 10^i 10^i · · · |i \in \mathbb{N}\}$ is rational and if a = bc and two of a, b, c are rational then the third is rational.

Thanks

  • 0
    The hint is incorrect. $0=\pi\cdot 0$, and $\pi$ is irrational.2011-09-06
  • 0
    @J.M., just looking at the titles, the two questions seem to me mutually converse. But I should really look at the body.2011-09-06
  • 2
    The question @J.M. linked only deals with half of the problem, but the answer posted by Bill links to the converse which is the other half. I am therefore voting to close as duplicate.2011-09-06

1 Answers 1