Why can't decimal numbers be represented exactly in binary?

Question

There have been several questions posted to SO about floating-point representation. For example, the decimal number 0.1 doesn\'t have an exact binary representation, so it\'

Answer 1

As we have been discussing, in floating point arithmetic, the decimal 0.1 cannot be perfectly represented in binary.

Floating point and integer representations provide grids or lattices for the numbers represented. As arithmetic is done, the results fall off the grid and have to be put back onto the grid by rounding. Example is 1/10 on a binary grid.

If we use binary coded decimal representation as one gentleman suggested, would we be able to keep numbers on the grid?