Determine whether the number $\frac{\pi}{5}$ is rational or irrational.

1. Problem Description

Determine whether the number $\frac{\pi}{5}$ is rational or irrational.

2. Solution Steps

A rational number can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$. An irrational number cannot be expressed in this form.

We know that $\pi$ is an irrational number. Multiplying or dividing an irrational number by a non-zero rational number results in an irrational number. Since $\frac{1}{5}$ is rational and $\pi$ is irrational, $\frac{\pi}{5} = \frac{1}{5}\cdot\pi$ is irrational.

3. Final Answer

Irrational