I heard somebody using 兩點九 and I thought he means 2:09. Actually, by 兩點九 he means 兩點九個字, or 2:45.
Does 兩點九 have two different meanings? Or does it always mean 2:45?
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It does not have two different meanings. It means 2:45.
We can also say 兩點四十五分。 In fact, it's more direct to say 兩點四十五分, if we're looking at a digital clock, since this is what is displayed. With a traditional clock with two hands and 12 numbers each representing a 5-minute period, 兩點九 or 兩點九個字 is more direct.
2:09 is 兩點零九分。
兩點九 is in traditional-chinese, with the missing characher "分" , implies Cantonese way of timing.
traditional-chinese is mainly used in HongKong/Taiwan/Macau.
simplified-chinese is used in mainland China.
Cantonese way of timing is used in HongKong/Macau and southern part of mainland China.
fuzzy and confusing ,are'nt they? a small table may help.
|Cantonese 2:45||两点九[个字]||not sure|
letters in () are utf-8 coding reference;
charachers in  can be omitted.