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

The problem is that you do not really know whether the number actually is exactly 61.0 . Consider this:

float a = 60;
float b = 0.1;
float c = a + b * 10;

What is the value of c? It is not exactly 61, because b is not really .1 because .1 does not have an exact binary representation.