When atoms are considered most of the mass lies in the nucleus which has neutrons and protons. Hence the statement is true because on comparing weight of neutron and proton to the mass of electron, mass of electron will be negligible.
The mass {atomic} of any material is actually the mass we get on adding masses of proton and neutron. Electrons are about 104 kg are lighter than the mass of proton Neutron in the mass of proton and neutron and nearly equal to each other.