# Small digitwise perturbations of a number make it normal to unrelated bases

## (*Lobachevskii Journal of Mathematics, Volume XI*)

Let *r, g ≥ 2* be integers such that log*g*/log*r* is irrational. We show that under *r*-digitwise random perturbations of an expanded to base *r* real number *x*, which are small enough to preserve *r*-digit asymptotic frequency spectrum of *x*, the *g*-adic digits of *x* tend to have the most chaotic behaviour.