Question

The reciprocal of the reciprocal of a number is

Answer 1

the same number, as long as the original number is different from zero.

Explanation:

Notice that the number zero doesn't have reciprocal (division by zero is not defined). Therefore, as long as the number is different from zero, the reciprocal of the reciprocal of the number is the number itself.

Here in math terms:

Reciprocal of the number "x" (with "x" different from zero) is:
`(1)/(x)`

the reciprocal of this is:

`(1)/((1)/(x) ) =1 / (1)/(x) = 1\,*(x)/(1) =x`

where we have used that dividing a number by a rational expressions is equivalent to multiplying the number by its reciprocal.