# What is the additive and multiplicative inverse of 0.4?

Feb 6, 2015

The answers are: $- 0.4 \mathmr{and} 2.5$

The inverse of 0.4 in the additive operation is that element ($a$) that added to 0.4 gives 0.

So:

$0.4 + a = 0 \Rightarrow a = - 0.4$

The inverse of 0.4 in the multiplicative operation is that element ($a$) that multiplied to 0.4 gives 1.

So:

$0.4 \cdot a = 1 \Rightarrow \frac{4}{10} a = 1 \Rightarrow \frac{2}{5} a = 1 \Rightarrow a = \frac{5}{2} = 2.5$.