Properties of Real Numbers: exemplo 1.126

To find the multiplicative inverse, we find the reciprocal.

1. ⓐ The multiplicative inverse of 9 is the reciprocal of 9, which is $\frac{1}{9}.$ Therefore, the multiplicative inverse of 9 is $\frac{1}{9}.$
2. ⓑ The multiplicative inverse of $-\frac{1}{9}$ is the reciprocal of $-\frac{1}{9},$ which is $\mathrm{-9}.$ Thus, the multiplicative inverse of $-\frac{1}{9}$ is $\mathrm{-9}.$
3. ⓒ To find the multiplicative inverse of 0.9, we first convert 0.9 to a fraction, $\frac{9}{10}.$ Then we find the reciprocal of the fraction. The reciprocal of $\frac{9}{10}$ is $\frac{10}{9}.$ So the multiplicative inverse of 0.9 is $\frac{10}{9}.$