[Solved] Is 1/3 a Rational, Irrational Number or an Integer?

Yes, $\dfrac{1}{3}$ is a rational number. In this post, we will learn how to prove $\dfrac{1}{3}$ is a rational number. At first, we first recall the definition of a rational number.

Definition of Rational Number

A number $x$ is called a rational number if it can be represented as $\dfrac{p}{q}$ where $p$ and $q$ are integers with $q \neq 0$.

Otherwise, the number $x$ is called an irrational number.

For example,

• $1$ is a rational number.
• $\pi$ is an irrational number.

Is $\dfrac{1}{3}$ a Rational Number?

Note that the number $\dfrac{1}{3}$can be written as $\dfrac{p}{q}$ where $p=1$ and $q=3 (\neq 0)$. Thus, by the above definition of rational numbers, we can conclude that $\dfrac{1}{3}$ is a rational number.

Conclusion: $\dfrac{1}{3}$ is not an irrational number.

Is $\dfrac{1}{3}$ an Integer or a Whole Number?

As $\dfrac{1}{3}$ represents a fractional value, it cannot be an integer. For the same reason, $\dfrac{1}{3}$ cannot be a whole number.

Few Remarks:

(1) $3/0$ is not a rational number as we have $0$ in the denominator.

(2) $3=\dfrac{3}{1}$ is a rational number as it can be expressed as $p/q$ where $p=3$ and $q=1 (\neq 0)$.

(3) $0=\dfrac{0}{1}$ is a rational number as it can be written as $p/q$ where $p=0$ and $q=1 (\neq 0)$.

(4) A real number can be either rational or irrational; it cannot be both at the same time.

(5) Every integer is a rational number, but the converse is not true. For example, $\dfrac{1}{3}$ is a rational number but it is not an integer.

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