As a consequence of Schmidt's Subspace Theorem, Adamczewski, Bugeaud, and Luca (2004) proved that the decimal expansion of an algebraic number cannot be too simple. In particular, if $b_0,b_1, \dots$ is a non-periodic automatic sequence on a finite alphabet, then the base $p$ number $0.b_1b_2\cdots$ is transcendental.
Kevin O'Bryant