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Pi is an irrational number, like many other irrational number (infinitely many, in fact), like square root of 2, square root of any non-square number (I think), and e, etc.
Irrational numbers do exist on the number line, so Pi would also be on the number line. Now you wouldn't be able to draw it at its exact location, but you wouldn't be able to draw the number 1 at its exact location either, because there's always inaccuracy in physical measurements (for example, you might use a ruler and draw number 1 at one inch, but then the ruler's lines have some thickness, so if you want to get even more accurate, you'll have to use an even smaller ruler, but that would also have some inaccuracy, and so on...)
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