Question & Answer

State the following statements are True or False.
The reciprocal of 0 lies on the real line.
  {\text{A}}{\text{. True}} \\
  {\text{B}}{\text{. False}} \\

ANSWER Verified Verified
Hint:-In this problem we have to examine whether the reciprocal of zero which is not defined exists on the number line or not.

Complete step-by-step answer:
Real Line or Real Number Line: It is a representation of all the real numbers on a horizontal line such that each point on the line corresponds to a real number and every real number corresponds to a point on the line.
Rational Number: Number which can be represents in the form of $\dfrac{p}{q}{\text{ where }}q \ne 0$
Since, Zero is the only rational Number that does not have a reciprocal as $\dfrac{1}{0}$ is not defined,
Hence, zero cannot be represented on a real line.
Therefore, Statement is false.
Hence, option B. is correct.

Note:- Whenever you get this problem the key concept to solve this is to remember that the reciprocal of every number exists on a real line except zero because its reciprocal is not defined.