# Is 6.416 an irrational number?

Dec 6, 2016

No, any terminating decimal number is rational.

#### Explanation:

The real numbers $\left(\mathbb{R}\right)$ consist of the union of the rational numbers $\left(\mathbb{Q}\right)$ and the irrational numbers $\left(\mathbb{Z}\right)$

Any number that can be expressed as a terminating or recurring decimal is rational - i.e $\in \mathbb{Q}$

A number $\in \mathbb{Z}$ cannot be expressed by a terminating decimal.

Hence, $6.416$ is $\in \mathbb{Q}$ and therefore $\neg \in \mathbb{Z}$