Parts-per-million is a form of concentration that is confusing to some. It is often used for aqueous solutions at low concentrations because, as you state in your question, in dilute solutions the density of water has not been affected ie. is still 1.00 g/mL.
parts per million is defined as micrograms of solute per milliliter of solution. This doesn't inherently make sense since micrograms are on the millionths scale, but mL are on the thousandth scale, so it would seem to be millionth per thousandth--Not so! Since the 1.00 mL of water weighs 1.00 g, ug/mL converts, for dilute aqueous solutions, to ug/g, which now makes sense as parts per million. So, from the information given, the calculation is quite simple:
