Question

What is the opposite and reciprocal of $0.2$?

Answer 1

Hint: To obtain the solution of the given statement we will use the additive and multiplicative inverse property of the numbers. Firstly we will find the opposite of the number by taking such a number which when added to it gives an answer as 0. Then for reciprocal we will divide 1 by the number and check whether the answers obtained when multiplied by the number give 1 as answer.

Complete step by step solution:
We have to find opposite and reciprocal of $0.2$
Firstly we will find the opposite of the number by additive inverse definition the opposite of $0.2$ when added to the number gives answer as 0.
So we can let the opposite number be $x$
Therefore by above statement we get,
$\begin{align}
  & 0.2+x=0 \\
 & \Rightarrow x=-0.2 \\
\end{align}$
So the opposite of $0.2$ is $-0.2$ which when added gives an answer as 0.
Next we will find the reciprocal of the number $0.2$ by dividing 1 by it as follows:
$\begin{align}
  & \Rightarrow \dfrac{1}{0.2} \\
 & \Rightarrow \dfrac{1}{\dfrac{2}{10}} \\
 & \Rightarrow \dfrac{10}{2} \\
 & \Rightarrow 5 \\
\end{align}$
So the reciprocal of $0.2$ is $5$ which when multiplied give answer as 1.

Hence the opposite and reciprocal of $0.2$ is $-0.2$ and 5 respectively.

Note: One condition that must be present if two numbers are opposite is that their sign should be opposite if one is positive another one should be negative. For reciprocal one number should be the upside down version of the other number. One mistake that usually happens in this type of question is that we find the opposite of the number and flip it to get one answer but in this question there is and written between opposite and reciprocal so we will get two answers separately.