Are you sure? Intuitively I would have said, that "I'm one eighty tall" is an abbreviation for "I'm one [meter] [and] 80 [centimeter] tall".
Thinking about it, if I measure something with a folding ruler, I would more naturally say "it's one meter eighty long" (German native speaker here, as already said elsewhere, with other languages YMMV).
But the point still stands. In metric, you can slap the numbers together or separate them, convert them to different units or sprinkle easily units in between or not. It all works. At worst it is just moving the decimal point around or adding/removing zeros. Very easily done in your head.
Well I suppose the nice thing about metric is that it doesn't matter!
You may be convincing me though, since in feet and inches it does matter, and it would mean as you say - 'looks about 10 11' means 10'11", not 1011".
In the UK though we generally don't mix metres and centimetres - '1 8' would mean '1.8' not '1.08', though I'd say the decimal point would rarely be elided, so that's clear.
So I just wouldn't say 1 80 about metres unless the question was 'how many metres' - and then I'd mean 180m.
But yes, that's exactly how you would say it in German. There might be some part of the brain reserved to parse that sentence as "I'm (one) (four and 80)" but this doesn't feel weird or confusing at all.
Telephone numbers on the other hand are more confusing. Luckily you don't need to say them out loud anymore these days.
Thinking about it, if I measure something with a folding ruler, I would more naturally say "it's one meter eighty long" (German native speaker here, as already said elsewhere, with other languages YMMV).
But the point still stands. In metric, you can slap the numbers together or separate them, convert them to different units or sprinkle easily units in between or not. It all works. At worst it is just moving the decimal point around or adding/removing zeros. Very easily done in your head.