We use parts per million to express the concentrations of solutions that contain very, very small amounts, often called trace amounts, of a given solute.
More specifically, a solution's concentration in parts per millions tells you the number of parts of solute present for every
10^6=1,000,000
parts of solution. You can thus say that a 1 ppm
solution will contain exactly 1 g of solute for every 10^6g of solution.
In this case, you know that you have
38 mg Pb x (1 g/10^3 mg) = 3.8 x 10^-2 g Pb
in exactly
300.0 g = 3.000 x 10^2 g solution
This means that you can use this known composition as a conversion factor to scale up the mass of the solution to
10^6 g solution x (3.8 x 10^-2 g Pb/3.000 x 10^2 g solution)
= 130 g solution
Since this represents the mass of lead present in exactly 10^6 g of solution, you can say that the solution has a concentration of:
concentration (ppm) = 130 ppm Pb