There's a rather infamous recorded phone call, from maybe 20 years or so ago, where a Verizon customer calls to customer support to complain that their material advertised a certain cellphone internet connectivity plan to cost ".002 cents per kilobyte", but he was charged 0.002 dollars (ie 0.2 cents) per kilobyte.
It's quite clear that the ad meant to say "$0.002 per kilobyte", but whoever had written the ad had instead written ".002c per kilobyte" (or ".002 cents per kilobyte", I'm not sure as I have not seen the ad). (It's also evident from the context that the caller knew this but wanted to deliberately challenge Verizon for their mistake in the ad, as false advertisement is potentially illegal.)
I got reminded of this when I recently watched a video by someone who, among other things, explained how much money one can get in ad revenue from YouTube videos. He explains that his best-earning long form video has earned him "6.33 dollars per thousand views", while his best-earning shorts video has earned him "about 20 cents per thousand views". Crucially, while saying this he is writing these numbers, and what does he write? This:
In other words, he says "twenty cents", but rather than write "$0.20" or, alternatively, "20 c", he writes "0.20 c".
Obviously anybody who understands the basics of arithmetic knows that "0.20 c" is not "20 cents". After all, you can literally read what it says: "zero point two zero cents", which rather obviously is not the same thing as "twenty cents". It should be obvious to anybody that "0.20 c" is a fraction of a cent, not twenty entire cents (in particular, it's one fifth of a cent). The correct notation would be "$0.20", ie. a fraction of a dollar (one fifth).
This confusion seems surprisingly common in the United States in particular, even among people who are otherwise quite smart and should know better. But what causes this?
Lack of education, sure, but what exactly makes them believe this? Why do they believe this rather peculiar thing?
I think that we can get a hint from that phone call to Verizon. During that phone call the customer support person, when explicitly asked, very explicitly and clearly stated that ".002 cents" and ".002 dollars" mean the same thing. When later in the call the manager took over the call, he said the exact same thing.
Part of this confusion seems to indeed be the belief that, for example, "20 cents", "0.20 cents" and "0.20 dollars" all mean the same thing. What I believe is happening is that these people, for some reason, think that these are some kind of alternative notations to express the same thing. They might not be able to explain why there are so many notations to express the same thing, but I would imagine that if asked they would guess that it's just a custom, a tradition, or something like that. After all, there are many other quantities that can be expressed in different ways, yet mean the same thing.
It gives credibility to this hypothesis that, also, in that phone call to Verizon, the customer support person repeatedly says that the plan costs "point zero zero two per kilobyte", without mentioning the unit. Every time she says that, the customer explicitly asks "point zero zero two what?" and she clearly hesitates, and then says "cents". Which, of course, is the wrong answer, as it should be "dollars". But she doesn't seem to understand the difference.
What I believe happened there (and is happening with most Americans who have this same confusion) is that they indeed believe that something like "0.002", or ".002", in the context of money, is just a notation for "cents", all by itself. That if you want to write an amount of "cents", you use a dot and then the cents amount. Like, for example, if you wanted to write "20 cents", you would write a dot (perhaps preceded by a zero) and then the "20", thus "0.20" all in itself meaning "20 cents". And if you wanted to clarify that it indeed is cents, you just add the "¢" at the end.
They seem to have a fundamental misunderstanding of what the decimal point notation means and signifies, and appear to believe that it's just a special notation to indicate cents (and, thus, that "20 cents" and "0.20 cents" are just two alternative ways to write the same thing.)
Of course the critics are right that this ultimately stems from a lack of education: The education system has not taught people well enough the decimal system and how to use it. Most Americans have learned it properly, but then there are those who have fallen between the cracks and haven't got the proper education on the decimal system and arithmetic in general.
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