1 mg/l = 1 ppm

Basically you have .001g of "stuff"(a milligram) in 1000 grams of water (a liter). .001 times 1000 equals one million. So if you have one milligram of anything in water, it's one part-per-million.

At least that's the way I read it. Didn't do my best work in chem class though. \:\(