TITLE: Which real numbers have two representations?
QUESTION [6 upvotes]: Are they only numbers that end with 9999... and 0000... after the dot or some other too? If so, can you give an example?

REPLY [11 votes]: Any rational number whose decimal expansion terminates, i.e., numbers of the form $$\dfrac{p}{2^m 5^n}$$ where $p,m,n \in \mathbb{Z}$ can have two different representations. For instance,
$$\dfrac75 = 1.4 = 1.3\bar{9}$$