Question

Which of the following is not a rational number?
A) $\dfrac{3}{17}$
B) $\dfrac{-4}{19}$
C) $\dfrac{0}{8}$
D) $\dfrac{3}{0}$

Answer 1

Hint: By the definition of rational number, it is in the form $\dfrac{p}{q}$ ,where $p,q\in I$ and $q\ne 0$. Using this definition, check all the options, which is not satisfying this definition.

Complete step-by-step answer:
We know that, If a number can be expressed in the form of $\dfrac{p}{q}$, where p, q are integers and $q\ne 0$ , the number is called a rational number.
Let us check all the options one by one whether they are satisfying this definition or not.
Option A) $\dfrac{3}{17}$ - It is in the form of $\dfrac{p}{q}$. Here p=3 and q=17, Both p and q are integers and $q\ne 0$. So, $\dfrac{3}{17}$is a rational number.
Option B) $\dfrac{-4}{19}$ - It is in the form of $\dfrac{p}{q}$ where p=-4 and q=19. Both p and q are integers and $q\ne 0$. So, it is also a rational number.
Option C) $\dfrac{0}{8}$ - It is in the form of $\dfrac{p}{q}$ where p=0 and q=8. Both p and q are integers and $q\ne 0$. So, it is also a rational number.
Option D) $\dfrac{3}{0}$- It is in the form of $\dfrac{p}{q}$ where p=3 and q=0. According to the definition of rational numbers q should not be equal to zero but here q=0. So, this is not a rational number.
Hence option (D) is not a rational number. So, Option (D) is the correct answer.

Note: Students can make mistakes by getting confused between p and q, which one should not equal to zero. Remember that in fraction form of rational numbers, denominators can’t be equal to zero.