Probability theory shows that including 105 molecules in a volume will allow the determination of density to within 1%.

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Probability theory shows that including 105 molecules in a
volume will allow the determination of density to within 1%. Thus,
a cube that contains 105 molecules should be large enough to
accurately estimate macroscopic properties such as density and
velocity. Find the length of a cube that contains 106 molecules.
Assume room conditions. Do calculations for (a) water, and (b)
air.