In order to calculate the parts per million you will need to know how many mg of solute is dissolved in 1000g (1L) of water.
#(0.001g)/(1000g)# = 0.000001
Multiplying 0.000001 by 1,000,000 gives a result of 1ppm.
Here is a video discussing this type of calculation. In the video, the number of moles of barium present in a 1L sample of water with a barium concentration of 2ppm is calculated.
2 ppm is the maximum allowable level for barium in drinking water in the US as established by the EPA .
Video from: Noel Pauller