Atomic weight and molecular weight are considered dimensionless numbers because they are relative quantities that express the ratio of the mass of an atom or molecule to a chosen reference mass.
The atomic weight of an element is the weighted average mass of its naturally occurring isotopes relative to the mass of a carbon-12 atom, which is assigned a mass of exactly 12 atomic mass units (amu). It is expressed as a ratio, such as 12.01 amu for carbon. Since it is a ratio of masses, the units cancel out, resulting in a dimensionless value.
Similarly, the molecular weight of a compound is the sum of the atomic weights of all the atoms in a molecule. It represents the ratio of the mass of a molecule to a chosen reference mass, which is usually the unified atomic mass unit (u) or the Dalton (Da). Again, the units cancel out, resulting in a dimensionless value.
By expressing atomic weight and molecular weight as dimensionless numbers, it allows for convenient comparison of relative masses without the need for specific units. This simplifies calculations and facilitates the understanding of stoichiometry and other chemical concepts.