# Rational Numbers

When you divide one integer by another the answer is not always another integer.

For example $3 \div 2$, $2$ goes into $3$ once but there is a remainder of $1$, so the result of this division is NOT an integer.

$3 \div 2$ can also be written as $\displaystyle{\frac32}$ or $\displaystyle{1\frac12}$ or $1.5$.

When an integer is divided by another integer (not zero) the answer is a rational number. The word rational comes from ‘ratio’.

The symbol used to represent rational numbers is $\mathbb{Q}$.

A rational number can be written as a fraction (or ratio) of integers.

##### Examples:

$$\frac14,\; \frac12,\; -\frac23,\; \frac51$$

Look at the last example above $\displaystyle{\frac51 = 5}$.

All integers are rational numbers as they can be written as a fraction with a denominator (bottom number of the fraction) of $1$.

Rational numbers can be written as decimals that either terminate (finish) or recur (repeat).

##### Example:

$$\frac14 = 0.25\quad\text{terminates,}$$ $$-\frac23 = -0.666666666666\ldots\text{ which we write as } -0.\dot{6},\text{ repeating or recurring.}$$