. How is the concentration of a solute present in trace amount in a solution expressed?

ppm or Parts per million  is a way of expressing the trace amount of solute in solution. Just as per cent means out of a hundred, so parts per million or ppm means out of a million. Usually describes the concentration of something in water or soil. 

Parts per million = ( Number of parts of the component / Total number of parts of all components of the solution ) × 10⁶ 
Suppose 1 mg of solute is present in 1 kg of solvent , it's concentration in ppm would be :
1 mg/1 kg x 10⁶ 
1 kg = 10⁶ mg
So, 1 mg/ 10⁶ mg x 10⁶ = 1 ppm