The numbers we can "easily" plot on a number line are the constructible numbers, those that the ancient greeks worked with that can be made with a ruler and a compass. The constructible numbers are a tiny tiny subset of all the real numbers. Being able to be esily found on a numberline is not part of the definition of a Real number. All the Real numbers are there on the numberline but being able to easily find them has nothing to do with being Real.