What is water hardness?
Water hardness is, at its most basic, the presence of certain minerals in water. Historically, water hardness was a measure of water’s ability to form lather during laundering. Harder water, due to it’s high calcium/magnesium content, would not lather as readily (or at all). For a long time there were many different scales for this, due to different countries with different languages measuring different chemical reactions.
Today we measure Total Hardness, the total amount of both calcium and magnesium in the water, in parts per million (ppm). There are also individual tests for magnesium hardness and calcium hardness. Total hardness is not useful for float tanks, since we add about 300,000ppm of magnesium sulfate to our water.
The measurement you would potentially find useful to your tank would be calcium hardness, and even that is not really necessary to monitor.
Why do we (usually) measure water hardness?
High calcium hardness can cause scaling, a crusty precipitation of excess calcium. This is especially harmful to water heaters, as calcium has an inverse temperature solubility; in water, calcium is exothermic, which means it gives off heat when combining with water. This also means that the warmer the water, the less calcium can remained dissolved in it. For this reason water heaters are particularly vulnerable to excessive scaling, which can cause the heater to work harder to less effect. This not only raises the cost of heating your water, but will ultimately result in the heater failing.