64-bit floats should be fine; I think that tweet is only sort-of correct.

The problem with floats-storing-money is (a) you have to know how many digits of precision you want (e.g. cents, dollars, a tenth of a cent), and (b) you need to watch out if you're adding values together.

Even if certain values can't be represented exactly, that's ok, because you'd want to round to two decimal places before doing anything.

Is there a monetary value that you can't represent with a 64-bit float? E.g. some specific example where quantization ends up throwing off the value by at least 1/100th of whatever currency you're using?