> In modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in month names, day-of-month names, and fixed phrases. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu (4th month), shichi-gatsu (7th month), and ku-gatsu (9th month) respectively. The on readings are also used when shouting out headcounts (e.g. ichi-ni-san-shi).
For names and fixed phrases, there's at least an argument that e.g. "shi" is just a part of the word historically descending from a then-current word for 4, as opposed to the word for 4 being different when it identifies April. (That argument definitely won't apply to headcounts, though.)
The decimal example made me curious whether decimal numbers like 4.79 might ever be written out in kanji rather than Arabic numerals. Decimals are enough of a recent foreign import that I might expect them not to have a native, character-based representation.
I don't fully understand it, but that is what a native speaker told me.
Paper is counted in "sheets" or "reams," for example. "I want a sheet of paper" is distinct from "I want a paper" -- outside of the context of a newspaper, the latter would be considered grammatically incorrect.
It's just that in Japanese, these are more or less standardized based on the kind of thing you're counting, so 個 for small, discrete objects, 匹 for small animals, 本 for long, thin things, 冊 for bound sheaves of paper, etc.
So as an example, an English interface could say something like "4 umbrellas", and the Japanese version could get away with something like "4 傘 [kasa, meaning 'umbrella']" if it's a list, but if it's in prose, you definitely need to be able to say "傘4本 [lit. umbrella 4-count-of-long-thin-object]" or something similar depending on the context.
>>> Japanese doesn't just have different measure words, but also different number words depending on the thing being counted.
You're talking about the measure words, not the number words.