Question

Describe as to why the number below is rational or irrational?

pi/4

Answer 1

The number \(\frac{\pi}{4}\) is an example of a rational number divided by an irrational number.

To determine whether \(\frac{\pi}{4}\) is rational or irrational, let's analyze the components:

1. **Rational Numbers:** A number is considered rational if it can be expressed as the quotient of two integers (i.e., in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\)).

2. **Irrational Numbers:** A number is considered irrational if it cannot be expressed as a fraction of two integers. \(\pi\) is a well-known irrational number, which means it cannot be represented as \(\frac{a}{b}\) where \(a\) and \(b\) are integers.

Now, when you divide an irrational number (\(\pi\)) by a rational number (4), the result is still irrational. This is a general property of numbers: dividing an irrational number by a non-zero rational number yields an irrational number.

Thus, \(\frac{\pi}{4}\) is irrational because it is derived by dividing an irrational number (\(\pi\)) by a non-zero rational number (4).