Question

Every integer is a rational number. Is this statement true or false?
(a) True.
(b) False.

Answer 1

Hint: In this question, we will use the definition of rational number and use integers in that definition to check if integers are rational numbers or irrational numbers.

Complete step-by-step answer:
We know that rational numbers are those numbers which can be represented in the form of $\dfrac{p}{q}$, where $p$ and $q$ are integer numbers and $q\ne 0$.
For example, $\dfrac{3}{2}$.
Now, integers will be a rational number if integers can be represented in the form $\dfrac{p}{q}$, where $p$ and $q$ are integer numbers and $q\ne 0$.
Also, we know that, 1 when divided by any number, rational or irrational, gives the same number.
Therefore, if we divide any integer by 1, it will give us the same integer back. This is also true for zero.
For example, $\dfrac{-4}{1}=-4,\,\dfrac{0}{1}=1$, etc.
Also, 1 is an integer and $1\ne 0$.
Therefore, we can represent any integer in the form of $\dfrac{p}{q}$, where $p$ will be the integer we take and $q$ will be 1.
For example, 5 can be represented as $\dfrac{5}{1}$, where $p=5$ and $q=1$.
Hence, we can say that every integer is a rational number.
Therefore, the correct answer is option (a).

Note: Alternative way to check if integers are rational or not is that all integers have terminating decimal expansion as they have no digit after decimal point, so integers are rational numbers.