Question

How many numbers have an absolute value of 0.

Answer 1

Hint: Now we know that the absolute value of any number is given by $\left| x \right|$ . Hence first we will try to solve the equation $\left| x \right|=0$ . Now to find how many numbers have absolute value of 0 we will find the number of solutions of the above equation.

Complete step by step solution:
Now let us first understand the absolute value of a number.
An absolute value of a number is simply the magnitude of a number. The magnitude of a positive number is the number itself. The magnitude of negative numbers is nothing but the number without the sign. The absolute value of a number is represented by $\left| x \right|$ . and the function is defined as $\left| x \right|=\begin{matrix}
   x,x\ge 0 \\
   -x,x<0 \\
\end{matrix}$ .
Now let us take an example to understand absolute value.
Let us say we want to find the absolute value of 2 and – 4.
Now since 2 > 0 we can say that the absolute value is 2 itself.
Now – 4 < 0. Hence the absolute value will be given by $-\left( -4 \right)=4$ .
Hence the absolute value of – 4 is 4.
Now we can easily say that if x and –x will give the absolute value as x.
Now let us say we have an equation $\left| x \right|=0$ .
Now - 0 and 0 are the same thing. Hence the only solution to this equation is x = 0.

Hence there is only one number which gives the absolute value as 0 and it is 0.

Note: Now note that the absolute value is also called modulus. Absolute value is nothing but the distance of the point from origin. Since we know that distance is always positive the absolute value is also always positive.