Question

Is $(\pi -{\displaystyle \frac{22}{7}})$ a rational or irrational or zero?

Answer 1

Hint: For solving this question first we will see the definition of rational and irrational numbers. Then, we can answer this question correctly without any doubt.

Complete step by step answer:
Given:
We have to tell whether $(\pi -{\displaystyle \frac{22}{7}})$ is rational or irrational or its value is zero.
First, we should know the definition of rational and irrational numbers.
For a number to be rational when we express a number in the form of ${\displaystyle \frac{p}{q}}$ , where $p,q$ are integers such that $q\ne 0$ . For example: $2,{\displaystyle \frac{4}{3}}$ and any integer are rational numbers. But when any number cannot be expressed in such form then, that number will be irrational. For example: $\pi ,e,\sqrt{2}$ are irrational numbers. Few properties related to rational and irrational numbers are as follows:
1. Product of a rational and irrational number is an irrational number
2. Sum and difference of a rational and irrational number is always an irrational number
3. Division of any rational and irrational number is always an irrational number
Now, we came back to our question of whether $(\pi -{\displaystyle \frac{22}{7}})$ is rational or irrational or its value is zero.
As we know that, ${\displaystyle \frac{22}{7}}$ is a rational number and $\pi$ is an irrational number. Then, according to the second property we can say that, $(\pi -{\displaystyle \frac{22}{7}})$ will be an irrational number.
Thus, $(\pi -{\displaystyle \frac{22}{7}})$ is an irrational number.


Note: Here, chances of making one mistake is very high and that is to answer zero directly because usually we take $\pi ={\displaystyle \frac{22}{7}}$ , but we should know that ${\displaystyle \frac{22}{7}}$ is not the exact value of $\pi$ and $\pi$ is an irrational number.