The standard atomic weight, often represented by the symbol \( A_r \), is a dimensionless quantity that expresses the average mass of an element's atoms, weighted according to the natural abundance of its isotopes. This value is typically based on the carbon-12 isotope, which is assigned a mass of exactly 12 atomic mass units (amu). Standard atomic weights are used primarily for elements in their natural isotopic mixtures and are typically listed in the periodic table.