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Recently, I have been trying to work on some philosophy that I am developing, and the subject of measurement has come up.

My question goes a bit like this:

Suppose that it turned out that when you measure point A to point B as exactly 100cm (one metre), there are actually three invisible centimetres (just an example number) in that 100cm. Therefore you would still be using the standard decimal system as reference, as it would still be described as a metre, but there are actually three extra centimetres so that you call it 103cm.

I have been told that this is not possible, and the reason I was given is: "one metre is one metre, it can't be 103 cm unless you were to change the whole system."

What I then tried to say, is that what if measurements of length actually measured matter to some degree. For example, we can say that we are measuring the length of matter from point A to point B. What if there was an extra 3cm of matter that we hadn't accounted for?

I got the same answer: that this would be impossible because a metre is a metre.

Can people at the physics forums explain why?