You have to be kidding. US money is broken down to :pennies, nickel (worth 5 pennies)Dime worth two nickel, quoter worth five nickels (or two and 1/2 dimes)
dollar coins coins are not used much. On the bills there is a one dollar and it is worth 100 pennies. (a courses side note this is the only that has been redesigned) a Five dollar bill, a ten dollar bill, twenty dollar bill, a fifty and 100.
There are $500 bill but I only seen it at the mint, wich has toures from 10am to 5:00pm.
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No, not all do. The proportionality constants that change the units will have units themselves.
All are units of volume.
All three are ratios which do not have units.
That all depends upon what your "units" are.
All areas should be measured in square units.