# Ex.1.5 Q3 Number System Solution - NCERT Maths Class 9

## Question

Recall, \(\begin{align}\pi \end{align}\) is defined as the ratio of circumference (say **\(c\)**) to its diameter (say **\(d\)**). That is \(\begin{align}{\rm{\pi = }}\frac{c}{d}.\end{align}\). This seems to contradict the fact that \(\begin{align}\pi \end{align}\) is irrational. How will you resolve this contradiction?

## Text Solution

**Steps:**

Writing \(\pi\) as \(\begin{align}\frac{22}{7}\end{align}\) is only an approximate value and so we can’t conclude that it is in the form of a rational. In fact, the value of \(\pi\) is calculating as non-terminating, non-recurring decimal as \(\pi=3.14159\dots\) Whereas

If we calculate the value of \(\begin{align}\frac{22}{7}\end{align}\) it gives \(3.142857\) and hence\(\begin{align}\pi\ne\frac{22}{7}\end{align}\)

In conclusion \(\pi\) is an irrational number.