Well, well. So the name... TIL.
FYI I believe it used to be legal in the UK (still is? Is it even possible with modern plastic currency?) to tear a note in half to pay half the value. My brother said he saw it once, used to pay a bus fair, a very long time ago.
There were two common types in the colonial era-- one had the monarch's portrait, and one had two globes between two pillars. Both types featured a coat of arms that if you squinted hard might have some quadrant lines in them, but they'd be raised-- making them harder to use as cut lines.
Aside from cutting the larger coins, Spanish territories also produced a lot of low-denomination silver coins. You can see this reflected in the scarcity of early US quarters; the 2-real coin was legal tender until 1857, so there was less pressure to produce quarters than dimes during the early years of limited mint capacity.
>“The dollar was divided into "pieces of eight," or "bits," each consisting of one-eighth of a dollar.”
From there it makes sense that if you needed to further subdivide an eighth of a dollar you could get another coin that is worth some fraction of an eighth of a dollar, and so on. But this starts to get a little weird because all of these other coins start using different metals and each of them have their own exchange rate that fluctuates.
In any event a decimalized currency was a big innovation. So much so that we think of anything else as baffling.
https://en.wikipedia.org/wiki/Spanish_dollar