Scientists routinely use units of parts per million, or ppm, to convey information about the concentration of dilute chemical solutions. A solution of one ppm has one part chemical per one million parts of total solution. For example, one gram of chemical in one million grams of solution would be one PPM. Labs also use the closely related units of milligrams per litre, or mg/L, to define concentrations. You can convert from ppm to mg/L if you know the mass per unit volume of your solution, otherwise known as the density.
Write out the ppm value of your solution concentration, replacing ppm with units of milligrams per kilogram. For example, if your concentration value is 28 ppm, you would write out 28 mg per kg. Since there are 1,000 mg in a gram and 1,000 grams in a kg, the mg per kg of solution is the same as ppm.
Divide the mg/kg concentration value you just wrote out by 1,000 -- the number of grams in a kilogram -- to convert it into units of mg per gram. In the case of 28 mg per kg, you would calculate 28/1000 = 0.028 mg per gram.
Multiply the value you just calculated by the density of your solution, in units of grams per millilitre. This calculation will give you the solution concentration in units of mg per ml. If the density of the solution in the example was 1.08 grams/ml, your calculation would be 0.028 times 1.08 = 0.0302 mg/ml.
Multiply this latest value by 1,000, the number of millilitres in a litre. This will convert your concentration reading to units of milligrams per litre. The example would have a final value of 0.0302 times 1,000 = 30.2 mg/L.
This assumes that the parts per million units you are using are on a mass per mass basis, which is very common when using ppm to describe solution concentration. In very dilute water solutions near room temperature, the density is very close to 1 mg/ml and so the ppm concentration is essentially equal to the mg/L concentration.