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

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## 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?

Video Solution
Number Systems
Ex 1.5 | Question 3

## 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.

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