For most people who didn't study in the US PPM might be a new way of expressing concentration of nutrients in the aquarium. I know it was for me when I started out reading about nutrients. Probably because the US doesn't use the decimal-based metric system, it lacks quick ways of converting. This has resulted in popular use of % ppt ( parts per thousand) ppm (parts per million) ppb ( parts per billion). And unfortunately PPM, is not a unit anymore than % is a unit. PPM is a dimensionless quantity.
In the aquarium hobby the meaning is:
1 ppm = 1 mg/L
In the strictest and correct sense
Just like 300% PO4- has no meaning, in the strictest sense, 300ppm PO4- has no meaning. Thus lacking a unit it is very ambiguous. Is 300ppm by volume ? by mass? by number of atoms? what?
Sometimes you may see ppt, which most often means parts per thousand or 1 / 1000.
1% - 1 part per hundred
1ppt - 1 part per thousand
1ppm - 1 part per million
Given that most solutions are largely water (big assumption) and that the density of water is ~1 kg/L at most common temperatures (an approximation) you get the following:
1 mg/L = 1 mg / 1 L ≈ 1 mg / (1 L × 1 kg/L) = 1 mg / 1 kg = 1 mg / 1000000 mg = 1 ppm by mass
And so, with an assumption and an approximation we ended up using ppm as a de facto unit of mass concentration in aquarium keeping. I would encourage you to write mg/L instead of ppm for clarity.