diagram of irrational number

irrational number is defined as a number that dont have the last digit in their writin'. such as pi, surd 2, sin(x). this type of number are categorized to be irrational. why?
becouse it cant be rationalized. or in the same meaning we purposed it to be express as a fraction of two integer.(natural number).

in the existence of line number, it is clear that by the virtue of cartesian coordinate, that the number are cant be picturized in line. it should be express in the square, cylinder or perhaps sphere.

 ya it is true that the number is a single number, regardless of what number either irr or rational. but how to draw 1.000000000000..... and 1.
first insight it's look like a simple matter, but try to think the 1 is not exactly is 1.0000000000.. each number have their own subset (e.g 1.0000000000089 is a subset of 1.000000000008, and 1.1 is a subset of 1) so the line diagram are cant be draw.