Why every real number is not a rational number?

Answer 1

A real number is one with no imaginary parts, i.e. one which does not involve i, the square root of -1. Some examples of real numbers are -10, 3/4, sqrt2, e, 2.777... . However, not all of these numbers are rational numbers. A rational number is one which can be expressed in the form a/b, where a and b are integers. So of the examples above, -10, 3/4 , and 2.7777... are rational numbers, as they can be written -10/1, 3/4 and 25/9 respectively. In contrast, Irrational Numbers are those which cannot be expressed in this form, common examples of which are square roots of non-perfect squares, or important constants such as pi or e.