Question

Is zero a rational number? Can you write it in the form pq,where p and q are integers and q ≠0?

Answer 1

Rational Numbers

A rational number is any number or a fractional number which can be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integer and denominator $q \neq 0$.

Let's head to the question now.

Yes, 0 is a rational number. It can be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. For example;

$\Rightarrow 0 = \frac{0}{1}$

$\Rightarrow 0 = \frac{0}{2}$

$\Rightarrow 0 = \frac{0}{3}$

Hence, zero is a rational number.

Answer 2

Rational Number

We know that, Rational number is the of ${\dfrac{p}{q}}$ where both ${p}$ and ${q}$ are integers. And ${q}$ is not equal to 0, (${q}$ ≠0).

Zero (0) is a rational number, because it can be written as 0 ÷ any integer (non other than zero). And we could see that it is in the form of ${\dfrac{p}{q}}$ where q(denominator) ≠ 0. Hence, Zero is a rational number.

Example :

• Let ${p}$ be '0'
• And ${q}$ be any integer (1,2,3,...-1,-2....)

Writing it in ${\dfrac{p}{q}}$ form,

$\sf⟹ {\dfrac{0}{1}}$, $\sf{\dfrac{0}{2}}$, $\sf{\dfrac{0}{-1}}$, $\sf{\dfrac{0}{-2}}$

And here q (the denominator) ≠ 0.

Hence, Zero is a rational number.