Hardness is dissolved calcium and magnesium — the pair behind kettle scale and stubborn soap scum. The trade reports both in a single currency, mg/L as CaCO₃: as if every hardness ion were chalk. The conversion is $\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}$ — read aloud: TH equals two-four-nine-seven Ca plus four-one-one-eight Mg.

The trap this lesson exists to spring: never add the raw numbers. Ca mg/L and Mg mg/L are different currencies, and magnesium — the lighter ion — buys MORE hardness per milligram, which is why its factor is the bigger one. Where those exchange rates come from is lesson four's story; spending them correctly is today's. Yardsticks worth keeping: under 60 is soft, past 120 is hard, past 180 the kettle files a grievance.