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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.

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