The grain is 64.8 mg — the mass of a barley seed, one of the oldest units still drawing a paycheque. Water-softener dials across North America speak grains of hardness per US gallon, while every lab report speaks mg/L as CaCO₃. One grain in one US gallon (3.785 L) works out to $17.118\ \mathrm{mg/L}$ — the crossing number, and the whole lesson.

mg/L to grains: divide by 17.118. Grains to mg/L: multiply. And keep the direction check running — dial numbers are SMALL (a very-hard 250 mg/L is only about 15 gpg), so landing on the dial should always shrink the number. If it grew, you crossed the bridge the wrong way.