Documented variations in the isotopic compositions of some chemical elements are responsible for expanded uncertainties in the standard atomic weights published by the Commission on Atomic Weights and Isotopic Abundances of the International Union of Pure and Applied Chemistry. This report summarizes reported variations in the isotopic compositions of 20 elements that are due to physical and chemical fractionation processes (not due to radioactive decay) and their effects on the standard atomic weight uncertainties. For 11 of those elements (hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine, copper, and selenium), standard atomic weight uncertainties have been assigned values that are substantially larger than analytical uncertainties because of common isotope abundance variations in materials of natural terrestrial origin. For 2 elements (chromium and thallium), recently reported isotope abundance variations potentially are large enough to result in future expansion of their atomic weight uncertainties. For 7 elements (magnesium, calcium, iron, zinc, molybdenum, palladium, and tellurium), documented isotope-abundance variations in materials of natural terrestrial origin are too small to have a significant effect on their standard atomic weight uncertainties.