Units are arbitrary. Consider, you wouldn't balk at me having a line that is 6 units long and then dividing it into three segments each 2 units long apiece.

But all I have to do is then say that the whole line is 1 unit. That automatically makes the segments 1/3 long each. Exactly. You can't say they were all exactly 2 units long but then refuse to accept them being 1/3 units long now. They didn't change their actual length simply by me using different units to represent that length.

So either no number can be exactly represented or they all can.