Question

What is the absolute value of $\dfrac{3}{10}$?

Answer 1

Hint: We will first check if the number is positive or 0. If yes, then the absolute value will be the same number. If the number is negative, then the absolute value will be its same number without any negative sign. Alternatively, we can also use the number line.

Complete step by step solution:
We know that the absolute value of any number is, nothing but, the distance of that point from the origin, on the number line. And since distance can never be a negative value, we can easily say that the absolute value is always greater than or equal to 0.
We can also define absolute value as the non-negative value, without any regard to the sign of that number.
An absolute value of the variable $x$ is represented as Mod $x$ or $\left| x \right|$.
Let us understand this concept with an example.
For points, 4 and -4, the number line is shown below,

Hence, we can say the absolute value of both 4 and -4 is equal to 4.
We also know that to find the absolute value of any number x, we have the following definition.
$\left| x \right|=\left\{ \begin{matrix}
   \begin{matrix}
   x, & x\ge 0 \\
\end{matrix} \\
   \begin{matrix}
   -x, & x<0 \\
\end{matrix} \\
\end{matrix} \right.$ .
So, this means that if the number is zero or positive, then its absolute value is the same number. And if the number is negative, then its absolute value is the negative of that negative number, that is, again a positive number.
Here, in this question, we need to find the absolute value of $\dfrac{3}{10}$.
We can see here that the number $\dfrac{3}{10}$ is positive. So the absolute value of $\dfrac{3}{10}$ will be the same number.
Also, when we plot $\dfrac{3}{10}$ on the number line, we will see that the distance of that point from origin will be $\dfrac{3}{10}$.
Thus, the absolute value of $\dfrac{3}{10}$ is $\dfrac{3}{10}$.

Note: Some students consider the absolute value function as the greatest integer function. We must not get confused between these two different terms. We must also remember that absolute value is also known as the Modulus operator.