# Is a fraction a real number, rational number, irrational number ?

Jun 28, 2015

A fraction of two integers is a rational number. It is also a real number.

#### Explanation:

Integers are the numbers: $0 , 1 , - 1 , 2 , - 2 , 3 , - 3 , \ldots$

Rational numbers are any number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \ne 0$. So $5$, $12.42$, $- \frac{17}{3}$ and $0$ are rational numbers.

There are infinitely many rational numbers, but they do not form a continuous line. The continuous line of numbers is called the real number line. It includes all the previous numbers we have mentioned, but also numbers like $\sqrt{2}$, $\pi$ and $e$, which are not rational.

Irrational numbers are any real numbers that are not rational.