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If a student did a calculation and used a mass of 3.0 kg, then we suggested
to do the calculation again but multiply the mass by 50%, they would not
multiply 50% times 3.0 kg and come up with 150.0 %kg [alas, some would, but
most would not].
Or thinking in reverse, they know that 1.5 kg / 3.0 kg is
0.5 (dimensionless) but we multiply by 100 and tack on percent and call it
50%.
John gave a list of a few of these dimensionless units. Is that an
exhaustive list? Can others think of better or other examples?
By the way, the number of atoms in an object is a dimensionless unit too.