Percentage and parts per million
A fraction like 1/25 or 0.04 is correct but hard to feel. The same composition said as a percentage, or as parts per million, is the same number scaled up so it can be read at a glance.
As a percentage
percentage = fraction × 100
As parts per million (ppm)
ppm = fraction × 1 000 000
Worked example — magnesium in magnesium oxide
Problem
20 g of magnesium oxide contains 12 g of magnesium. Find the mass fraction and the mass percentage of magnesium.
Solution
mass fraction of magnesium = 12 g ÷ 20 g
= 0.6
mass percentage of magnesium = 0.6 × 100
= 60%
What parts per million is for
Some compositions are so small that a percentage is all zeros after the point. A pollutant in drinking water or a trace metal in a soil sample might be 0.000 003 as a fraction, which is 0.0003% — awkward to read and easy to mistype. The same figure is 3 ppm, which is a number you can hold in your head and compare against a limit.
Both are still the same fraction
Multiplying by 100 or by a million does not change the composition, only the units it is quoted in. A percentage and a ppm figure can both be turned straight back into the fraction they came from.
Mass fractions, volume fractions and mole fractions can each be expressed as a percentage or as parts per million. The choice is about how small the number is, not about what kind of fraction it is.