Question

Is $\pi $ a rational number? Justify your answer.

Answer 1

Hint: To solve this question first we need to recall the definition of rational and irrational numbers. Then, we analyze the values of $\pi $ which are $\dfrac{22}{7}$ and $3.14$ to reach the desired answer.

Complete answer:
We know that a number of the form $\dfrac{p}{q}$ is called a rational number, where p and q both are integers and $q\ne 0$ i.e. the denominator of a fraction cannot be equal to zero. Also, p and q individually cannot be any decimal or fraction numbers.
Irrational numbers are numbers that cannot be expressed as a fraction or as a ratio of two integers.
Now, we know that $\pi $ is a mathematical constant and is defined as the ratio of a circle’s circumference to its diameter.
$\pi $ has approximate values in rational number $\dfrac{22}{7}=3.14285........$
So, we get that $\pi $ has a never ending, infinite value which is non-terminating and non-repeating. So, it certainly does not exist on any number line.
So, we can conclude from the above discussion that $\pi $ is an irrational number.

Note:
Students may consider the value of $\pi $ as $\dfrac{22}{7}$ and give the answer. As $\dfrac{22}{7}$ is a rational number and students give the answer i.e. yes $\pi $ is a rational number but it is a wrong answer. Students have to analyze both the values of $\pi $ and then reach any conclusion. As $\pi $ is used in many formulas in mathematics and physics, so when we put the value of $\pi $ we get approximate answers.