## Are all fractions rational numbers?

No.

A rational number can be expressed in the form $\displaystyle\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. In other words, it is a fraction whose denominator is not zero, and both the denominator and numerator are integers.

Some fractions, however, may contain a numerator or denominator that is not an integer. Some examples of such fractions are

$\displaystyle\frac{\sqrt{3}}{2}$, $\displaystyle\frac{\pi}{4}$ and $\displaystyle\frac{e}{2}$.

A rational number may be represented in many ways, but it can always be expressed as a fraction. For instance, $10^{-1}$ is a rational number because we can express it as $\frac{1}{10}$. Also, the number $0.333 \cdots$, a repeating decimal, is  a rational number because we can also express it as fraction $\frac{1}{3}$.