Question

Can we write $0$ in the form of $\dfrac{p}{q}?$

Answer 1

Hint: In this question we have to write zero i.e. $0$ in the form of $\dfrac{p}{q}$ . So to write zero in the ratio form of p and q, we should note that p must be equal to zero,
$p = 0$ and the denominator $q$ can be any rational number apart from zero, because we know that any number divided by $0$ is an undefined operation. So we will keep this in mind and solve the question.

Complete step by step answer:
As we can see that we have to write $0$ in the form of $\dfrac{p}{q}$ in such a way that
$p = 0,q \ne 0$ .
Now we know that a rational number is defined as the number that can be expressed in the form of $\dfrac{p}{q}$, where $q \ne 0$ .
So we can say that we have to write zero in the rational number form.
Let us take the first rational number
$1$
So we can say that we have
$p = 0,q = 1$
Now we can write this in the fraction form:
$\dfrac{p}{q} = \dfrac{0}{1}$
We will take another rational number
$3$
Here we have
$p = 0,q = 3$
Again we can write this in the fraction form:
$\dfrac{p}{q} = \dfrac{0}{3}$
Hence we can say that $0$ can be written in the form of $\dfrac{p}{q}.$

Note:
1. We should note that in a rational number, when a fraction is divided, the result will be in the form of decimal, that may be either repeating decimal or terminating decimal. In the above solution, we have the value of
$\dfrac{0}{1} = \dfrac{0}{3} = 0$ , Because zero when divided by another number is equal to zero.
2. We should keep in mind that here the denominator (q) should not be equal to zero which results in indeterminate form $\dfrac{0}{0}$.