The problem is that some decimal amounts, e.g. 10 cent ($ 0.10) cannot be represented precisely using binary floating point. It doesn't matter how many bits you use since 0.1 have an infinite expansion in binary.

This is exactly what the article describes and explains. 10 cent plus 20 cent does not equal 30 cent, when using binary floating point. This is not acceptable in accounting, since at one point the error may accumulate and cause an error at the size of a cent (or more).