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

Last updated date: 13th Jun 2024
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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.