Question

Is $10$ rational or irrational?

Answer 1

Hint: First, we shall analyze the given problem so that we are able to solve it. Here, we are given a number $10$ and we need to find whether $10$is a rational number or an irrational number. Before getting into the answer, we should know what is a rational number and what is an irrational number. If we learn about it, we can easily answer.

Complete step-by-step answer:
A rational number is a number that must be expressed as some fraction and also as a positive number, a negative number, and zero and we can write a rational number mathematically as $\dfrac{p}{q}$ , where $q$ is not equal to zero and $p$, $q$are integers.

When the given number is not rational ( not in the form of $\dfrac{p}{q}$ , where $q$ is not equal to zero and $p$ , $q$are integers), we call that number an irrational number. Also, the irrational numbers have endless non-repeating after the decimal point where that decimal number is changed into fractions.
Here we are given a number $10$.

Now, we shall write this number as follows.
$10 = \dfrac{{10}}{1}$
We can note that both $10$ and $1$are integers and the denominator is not equal to zero.
Hence, we can conclude that $10$is a rational number.

Note: Some examples of rational numbers are listed as follows.
a) $4$ is a rational number because $4$can be written as $\dfrac{4}{1}$ where $4$and $1$ are integers.
b) $\dfrac{3}{2}$ is a rational number because $3$ and $2$ are integers.
Some examples of irrational numbers are listed as follows.
a) $\dfrac{2}{0}$ is an irrational number because the denominator is equal to zero.
b) $\sqrt 3 $ is an irrational number because $\sqrt 3 = 1.732050808$ having endless digits after the decimal point.