Rounding would only occur towards the end of the number to make it fit into the required "fraction" section
you are quite correct. Is it then your conclusion that since the rounding occurs way out in the less significant digits (or bits) that the equality should work? I think you are missing my point still. When you say
that which is referred to as the "fraction" is just the number stripped of the decimal point
you seem to be implying that this is true for fractions, but as I have demonstrated, it is not. You are taking a statement which is true for whole numbers and applying it to fractions, where is is NOT true and yet you still seem to believe it is true.

The point is that decimal fractions will NOT always store precisely in binary. How about decimal fractions in a decimal computer? Well, suppose we HAD a decimal computer and wanted to add 1/9 plus 8/9 and compare the result to 1.0 --- WE WOULD GET INEQUALITY. Think it through.