Question

What is the absolute value of 0?

Answer 1

Hint: Absolute value represents the distance of a number from 0 on the number line. The absolute value of a positive or negative number is positive. We can denote absolute value of a number, say a, as $abs\left( a \right)$ or $\left| a \right|$ . We have to find $\left| 0 \right|$ .

Complete step by step solution:
We have to find the absolute value of 0. Let us see what is meant by absolute value. Absolute value represents the distance of a number from 0 on the number line. The absolute value of a positive number is positive. Absolute value of a negative number is always positive. We can say that the absolute value of a number ignores its negative sign. We can denote absolute value of a number, say a, as $abs\left( a \right)$ or $\left| a \right|$ . We call $\left| {} \right|$ as modulus. Also, we can write $\left| a \right|=a$ and $\left| -a \right|=a$ .
Now, let us write the absolute value of 0. We can denote it as $\left| 0 \right|$ .
$\Rightarrow \left| 0 \right|=0$
From the above value, we can say that the distance of 0 from 0 is 0.
Hence, the absolute value of 0 is 0.

Note: Students must note that the absolute value ignores negative sign is due to the fact that distance cannot be negative. We commonly denote the absolute value as $\left| {} \right|$ . There are many properties associated with absolute value. We can represent absolute value of x in the form of a function as
$\left| x \right|=\left\{ \begin{matrix}
   x,\text{ if }x\ge 0 \\
   -x,\text{ if }x<0 \\
\end{matrix} \right.$