Question

Is $9$ a rational number?

Answer 1

Hint: Use the definition of rational numbers given by “Any number having the form $\dfrac{p}{q}$ where ‘p’ and ‘q’ both are integers and $q\, \ne 0$ is known as Rational Number” As a boundary conditions to decide whether the numbers are rational or not.

Complete step-by-step answer:
In the above question,
To identify that which number is a rational number, we should know the definition of rational number so that we can verify the conditions of rational numbers and conclude whether the number is rational or not, and for that we should know the definition of rational numbers given below,

Definition of Rational Numbers:
Any number having the form $\dfrac{p}{q}$ where ‘p’ and ‘q’ both are integers and $q\, \ne 0$ is known as Rational Number.
We can also write $9$as $\dfrac{9}{1}$.
Now, if we compare $\dfrac{9}{1}$ with $\dfrac{p}{q}$ we get $p = 9$ and $q = 1$.
Therefore, p and q both are integers and q is not equal to zero.
Hence, $9$ is a rational number.

Note: As per the definition of rational numbers they should have the form $\dfrac{p}{q}$ where $q\, \ne 0$ that means ‘q’ can be 1 also and if q is equal to one the all the integers are also rational numbers including zero on the numerator. So, if you find an integer in the option in this type of problem, don’t get confused and write it as a rational number.