Bounds to atomic information entropies and their sum in position and momentum spaces have been derived in terms of radial and momentum expectation values [r(n)] and [p(n)]. Numerical studies on atomic systems show that the bounds presented in terms of [r] and [p], the first moments of the position and momentum space densities are sharper than those given by Gadre and Bendale in terms of [r(2)] and [p(2)], the second moments of the position and momentum space densities, Within the BKCM procedure due to Burkhardt, Konya, Coulson, and March, several relationships between the information entropies and the average electron densities [rho] and [gamma] in position and momentum spaces have been established.