What are Real Numbers?

In short

Real numbers are all the numbers on the number line: the rational numbers, which can be written as a fraction, and the irrational numbers, which cannot.

In simple words

A rational number such as $\dfrac{3}{4}$ or $0.25$ has a decimal that ends or repeats. An irrational number such as $\sqrt{2}$ or $\pi$ has a decimal that never ends and never repeats. The decimal of $\dfrac{1}{7}$ is $0.\overline{142857}$ , which repeats, so it is rational. Natural numbers, whole numbers, integers and rational numbers all sit inside the real numbers. Operations on real numbers follow the same rules: commutative, associative and distributive.

Example

$\sqrt{9} = 3$ is rational, but $\sqrt{8} = 2\sqrt{2}$ is irrational. The cube root of $2$ is also irrational.

Also searched as: operations on real numbers, decimal of 1/7, cube root of 2.