# What is the difference between real numbers and rational numbers?

Apr 2, 2016

Although all rational numbers are real numbers, there are some numbers (irrational numbers) which are not rational numbers.

#### Explanation:

Rational are those numbers which can be written as a ratio of two integers, the denominator being non-zero.

Real numbers are those, which can be represented on real number line.

Although all rational numbers can be represented on real number line, there are numbers which are not rational numbers but can be represented on real number line too.

Numbers like $\sqrt{2}$, $\sqrt{x}$ (where $x$ is a positive rational number but not the square of a rational number), $\pi$ etc. cannot be expressed as ratio of two integers like rational numbers, but can be represented on real number line. These numbers are called irrational numbers.

Hence, though all rational numbers are real numbers, there are some numbers (irrational numbers) which are not rational numbers.