Question

Is pi a rational or irrational number?

Answer 1

Verifying whether $\pi$ is a rational or an irrational number:

Rational numbers are the numbers which can be expressed in the form $\frac{p}{q}$ where $p,q$ are both integers and $q\ne 0$.

When expressed in decimal form, rational numbers are terminating decimals or repeating in an fixed pattern

For example:

1. $\frac{10}{3}=3.3333...$ is a non terminating yet repeating type of rational number.
2. $\frac{27}{4}=6.75$ is a terminating rational number.

Irrational numbers are numbers which cannot be expressed as a ratio of two integers.

When expressed in decimal form, they are non terminating and non repeating.

$\pi$ is the ratio of a circle's circumference to a diameter. It is a constant value which is approximately equal to $3.14159265359.....$

$\pi$ is non terminating non repeating sequence of numbers and cannot be expressed as the ratio of two integers.

Hence, $\pi$ is an irrational number.