What are the Similarities between rational and irrational number?

Answer 1

The one thing they have in common is that they are both so-called "real numbers". You can think of them as points on the "real number line".Both are infinitely dense, in the sense that between any two rational numbers, you can find another rational number. The same applies to the Irrational Numbers.

Thus, there are infinitely many of each. However, the infinity of irrational numbers is a larger infinity than that of the rational numbers.

Answer 2

Both sets are subsets of real numbers. Together the form a field and so the members share all the properties of a mathematical field.

Answer 3

They are both real numbers.