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

If you make a big enough number with floating point (as it can do exponents), then you'll end up with inexactness in front of the decimal point, too. So I don't think your question is entirely valid because the premise is wrong; it's not the case that shifting by 10 will always create more precision, because at some point the floating point number will have to use exponents to represent the largeness of the number and will lose some precision that way as well.