Be careful, though, as if I type “per” instead of using “/” I get an answer like 0.39 US fluid ounces per gallon – for some reason, it doesn’t interpret the question right and gives the answer to 50/128 instead of 128/50.
When both of the measures are in the same unit, you can substitute any unit.
2 gallons per 100 gallons will give you the same dilution as 2 cups per 100 cups, or 2ml per 100ml or two eggcups per 100 eggcups (notwithstanding the complication that smaller units are a bit harder to measure accurately)
To be fair, at least English volumetric measurement from tablespoons on up to gallons is base-2, which is maybe not quite as convenient as base-10, but is sane in a way that distance measurements are very much not.
There are many powers-of-2, but I am not convinced it is the real rationale. For example, while a (fluid) ounce is indeed divided into 8 fluid drams, one should not overlook the fact that a dram then equals 3 scruples. Another example is that the introduction of the Imperial Standard Gallon [i.e., 10 pounds of water] in 1824 led to a division of an (Imperial Standard) pint into 20 fluid ounces. Most of all, though, if we look beyond England and Britain, the Roman weight and volume system all this is inspired by had many convenient fractions, but the denominator was by no means uniformly equal to 2, even leaving aside differing European interpretations which further confuse the issue.
Sure, but the point is that very often you’re not going to use the same units for the solute and the solvent. The 50:1 ratio in this case means that the quantities of the two lie in different ballparks and hence different units suggest themselves - as in the case of the OP, who wanted to measure the solute in ounces and the solvent in gallons. The advantage of the metric system here is that even where different units are used, these relate to each other by powers of ten. The metric ballpark unit corresponding to the gallon is the litre; the ballpark unit corresponding to the ounce is the millilitre or centilitre. It’s easy to figure out that a 50:1 ratio requires 2 centilitres or 20 millilitres of solute per litre of solvent.
I’ve never measured something in a dram or a scruple, so while you are I’m sure correct that historically it was all nonsense, as it exists now it’s all powers of two. Tablespoon x4 = ounce x8 = cup x2 = pint x2 = quart x4 = gallon.
Not… consistent powers of two, but still powers of two. Until you get to, like, acre-foot or something.
As far as I can tell, the US Customary measures doesn’t have a unit above gallon for fluid measurements. Or at least nothing in between gallon and acre-foot. Not sure why, since it has about a dozen different ones smaller than gallon.
ETA: there is the barrel, but that is not a standard unit. There’s a number of different barrels depending on what you’re measuring. And don’t even think about bringing up the firkin or hogshead or …
Because it’s not a power of two. Again, I’m not saying that the English volume measurement system is some well-designed paragon of reason. Just that the vast majority of it is not crazy, the way that distance measurement is.