Question

Fill in the blanks:
The number 0 is ______ the reciprocal of any number.

Answer 1

Hint: Here we will simply use the concept of reciprocal. First, we will write the basic condition of the reciprocal. Then we will write the reciprocal of 0 and using this we will complete the given sentence. The reciprocal of a number can be obtained by dividing 1 by the number itself.

Complete step by step solution:
Reciprocal is also defined as a multiplicative inverse because when a number is multiplied by its reciprocal it always gives 1. We know that if a number \[x\] is the reciprocal of the other number \[y\] then that other number \[y\] will also be the reciprocal of the number \[x\].
We know that the number 0 does not have any reciprocal because the reciprocal of 0 is equal to the infinity which does not exist.
\[\dfrac{1}{0} = \infty \]
Therefore, the reciprocal of number 0 doesn’t exist and it is not the reciprocal of any number either.

Hence, the number 0 is not the reciprocal of any number.

Note:
Here we have found out that the reciprocal of number 0 doesn’t exist but the reciprocal of infinity is equal to 0. We can find reciprocal of any real number like fractions and decimal numbers. For finding the reciprocal of a fraction, we just interchange the numerator and denominator. For example, the reciprocal of \[\dfrac{5}{4}\] is equal to \[\dfrac{4}{5}\]. Here, we have just interchanged the position of the number. To find the reciprocal of a decimal number, we just divide 1 by the given decimal number.