## Intermediate Algebra (6th Edition)

The reciprocal of a number $a$ is the number$\frac{1}{a}$, such that $a\times\frac{1}{a}=1$. When $a=0$, $\frac{1}{a}=\frac{1}{0}$, which is undefined (as you cannot divide a number by 0). Therefore, the number 0 has no reciprocal because there is no number, that when multiplied by 0, has a product of 1.