We investigate how nonzero rational multiplication and rational addition affect normality with respect to Q-Cantor series expansions. In particular, we show that there exists a Q such that the set of real numbers which are Q-normal but not Q-distribution normal, and which still have this property when multiplied and added by rational numbers has full Hausdorff dimension. Moreover, we give such a number that is explicit in the sense that it is computable.

Research of the first and second authors is partially supported by the U.S. NSF grant DMS-0943870.