TITLE: Question on the decimal expansion of algebraic numbers
QUESTION [5 upvotes]: Is the countability of the set of irrational algebraic numbers somehow reflected in a characteristic property of their decimal expansions?

REPLY [2 votes]: Well, something may be said for sure: decimal expression of irrational algebraic number can not have too many small periodic blocks in a row (like 0.1239239239239...), since it would imply the existence of too good rational approximations and so contradict the Roth's theorem.