Question

Which of the following rational numbers does not have a reciprocal?
A. 1
B. -1
C. 0
D. none

Answer 1

Hint: In order to determine the correct option, find out the reciprocal of every given option , you will see that the for the options A and B the reciprocal exists and for the option C which is zero ,the reciprocal does not exists as there is no such number when multiplied with zero gives 1 and also $ \dfrac{1}{0} $ is undefined.

Complete step by step solution:
In this question, we are given three options $ 1, - 1,0 $ and we have to find out of these numbers whose reciprocal is not possible.
Let us first figure out what is reciprocal of any number and how to find it.
So, reciprocal of any number is nothing but the multiplicative inverse of that number such that when you multiply the reciprocal with the original number you will get the result as $ 1 $.
To find the reciprocal of any number $ a $, we have to divide the number with $ 1 $. We get the reciprocal as
 $ \dfrac{1}{{number(a)}} $
Now let’s see every option given to us in the question to check whether its reciprocal is possible or not
First option is $ 1 $ . The reciprocal of $ 1 $ will be $ \dfrac{1}{1} = 1 $ .Therefore it exists
Second option is $ - 1 $ . The reciprocal of $ - 1 $ will be $ \dfrac{1}{{ - 1}} $ .
Third option is $ 0 $ . As we know zero does not have a reciprocal as there is no such number when multiplied with zero can be equal to $ 1 $ . And if I try to see what will be the reciprocal, so it will be $ \dfrac{1}{0} $ which is undefined. Hence , it clearly means that no reciprocal of zero exists.
Therefore, the correct option is (C).
So, the correct answer is “Option C”.

Note: 1. multiplication of a number with its reciprocal is always equal to 1.
2.Reciprocal of infinity is a perfect zero, i.e. $ \dfrac{1}{\infty } = 0 $
3.The domain for reciprocal function is real numbers except zero.