Question

Which of the following is an Irrational Number:
A. $\pi $
B. $\sqrt{9}$
C. $\dfrac{1}{4}$
D. $\dfrac{1}{5}$

Answer 1

Hint: Try to recall the definition of rational and irrational numbers and the examples of irrational numbers.

Complete step-by-step answer:
Before moving to the options, let us talk about the definitions of rational numbers followed by irrational numbers.
So, rational numbers are those real numbers which can be written in the form of $\dfrac{p}{q}$ such that both p and q are integers and $q\ne0$ . In other words we can say that the numbers which are either terminating or recurring when converted to decimal form are called rational numbers. All the integers fall under this category.
Now, moving to irrational numbers.
Those real numbers which are non-terminating and non-recurring are termed as irrational numbers.
The roots of the numbers which are not perfect squares fall under the category of irrational numbers. $\pi \text{ and }e$ are also the standard examples of irrational numbers.
So, let’s talk about the options.
The first option is $\pi $ and $\pi $ is an irrational number making option (a) correct.
However, let’s discuss the other options as well.
The second option is $\sqrt{9}$ and 9 is a perfect square hence, we can say that it is rational.
Option (c) and (d) are similar and are of the form $\dfrac{p}{q}$ with both p and q are integers and $q\ne0$ making both the options rational.
Hence, the correct answer is option (a) $\pi $.

Note: Don’t get confused with the value of $\pi $ as $\dfrac{22}{7}$ or 3.14 these are the approx. values of $\pi $ that we use for the sake of calculations but in actuality it is an irrational number.