Oh, and to be complete: The reason why multiplying by 100 = 2^2 * 5^2 helps when dealing with cash is that 0.20 isn't exactly representable in a finite-length binary number (since that's 1/5, and 5 isn't a power of two). It's the multiplication by 5^2 = 25 that makes previously inexact things exact. The additional multiplication by 2^2 = 4 just moves the decimal place by two digits, nothing the FPU couldn't have done on its own. You could represent cash in units of four cents (or two cents, or 256 cents) instead of one cent, and the result would be unchanged except for the location of the decimal place.
There is no useful, general analogy to this in numerical analysis. If you're using any fixed-sized representation of numbers--floating point, fixed point, or otherwise--then some ways to calculate an expression will be less accurate than others. You can avoid this with variable-length representations, but then some ways are slower. There is no way to avoid thinking about numerical conditioning.
There is no useful, general analogy to this in numerical analysis. If you're using any fixed-sized representation of numbers--floating point, fixed point, or otherwise--then some ways to calculate an expression will be less accurate than others. You can avoid this with variable-length representations, but then some ways are slower. There is no way to avoid thinking about numerical conditioning.