Such small amounts of mass, of course, cannot be weighted on any scale, but only determined indirectly via complicated apparatus.
In chemistry the enormous number 6.1023 has become a standard number and is frequently applied. The first who invented and used it, was Avogadro. So the number is also called:

Number of Avogadro = 6.1023

Two new units for masses or amounts have been introduced in chemistry:
  1. one micro-unit for the very small particles (atoms, molecules, ions, electrons). This micro-unit is a unit of mass: the 'atomic mass unit', amu, or: UNIT
  2. one macro-unit for such big numbers of small particles that they can be weighted on a normal scale. This unit, MOL, is a unit of numbers.

    One MOL is 6.1023

Keep in mind the following numbers: a pair, a dozen, a gross, a mol;

Note that you should not confuse the chemical concept mol with the biological mole.
We write both MOL and mol.