# Rational Numbers

Any number that can be written as a
fraction
with
integers
is called a
**
rational number
**
.

For example, $\frac{1}{7}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\frac{3}{4}$ are rational numbers.

(Note that there is more than one way to write the same rational number as a ratio of integers. For example, $\frac{1}{7}$ and $\frac{2}{14}$ represent the same rational number.)

All
*
integers
*
are rational numbers.

The number $-8$ is a rational number because it can be rewritten as $-\frac{8}{1}$ .

The number $0$ is a rational number because it can be rewritten as $\frac{0}{1}$ .

All mixed numbers are rational numbers.

$3\frac{1}{5}$ is a rational number because it can be re-written as $\frac{16}{5}$ .

All
*
decimals
*
which either terminate or have a repeating pattern after some point are also rational numbers.

The number $0.2$ is a rational number because it can be re-written as $\frac{1}{5}$ .

The number $0.\text{33333}\dots $ is a rational number because it can be re-written as $\frac{1}{3}$ .

Some numbers can't be rewritten as a fraction with integers, and so they are not rational numbers. Some examples are $\pi $ and the square root of any prime number. These are called irrational numbers.