Symantics of parts per (million, billion, etc) I have always thought that parts per million meant that in a solution of one million particles, one of those particles is the particle that you are looking for its concentration in ppm. However looking at the formula ppm=(mass solute/mass solution)* 1 million, it seems like it may be meaning one part of mass per mass of solution?
Doing a example calculation for one atom of mercury in 999,999 molecules of water, I get about 11 parts per million and not the 1 ppm. It seems like the ppX changes with molar mass of the X. Am I missing some key concept here or do I have the right idea. Thanks

(1 atom Hg)(mol Hg/Avogardros#)(20.59g/mol Hg)= 3.3309E-22g Hg = variable A

(999,999 molecules H2O)(mole H2O/ Avogardros#)(18.015g/mol H2O)= 2.9915E-17g H2O=variable B

ppm=(moles solute/moles solution)*10^6
ppm=A/(A+B) *10^6 = 11.13ppm
The notation "parts per" is just a dimensionless unit to describe small amounts.
In chemistry it's used for concentrations of dilute liquids.. whereas in physics it can be used for defining change with respect to another quantity and in Six sigma it's used to define "defects per million opportunities".

In chemistry however, $ppm$ is mostly used as concentrations of dilute solutions in water and sometimes used interchangeable with $mg/l$. The notion of "one particle per million particles of solvent" can be used for solid-solid solutions or initial understanding of the term.