Question

What is the sign of Modulus?

Answer 1

Hint: Before going to directly answer, we first discuss what modulus is. Now, modulus of what we will find: modulus of number or modulus of a variable or anything. Actually, modulus refers to absolute value or magnitude, or numeric value.

Formula used: \[\left| a \right| = a\] for any real value.
\[\left| x \right| = \left\{ \begin{array}{l}x;x \ge 0\\ - x;x < 0\end{array} \right.\], \[x\] is any real value.

Complete step-by-step solution:
Before going to a direct answer, we first discuss what modulus is. Now, modulus of what we will find: modulus of number or modulus of a variable or anything. Actually, modulus refers to absolute value or magnitude, or numeric value.
The modulus of a number is always positive. The given number may be negative or zero or positive. But after taking modulus over that given value we will have only a positive value. Modulus gives the numeric value of the given number, not its sign. Suppose, we have a number\[ - 4\]. If we take modulus of this number then we will have\[\left| { - 4} \right| = 4\]. Again, if we take another number like \[4\] then \[\left| 4 \right| = 4\]. The given numbers \[ - 4\] and \[4\] are different. But their modulus is the same. So, generally, we can generate the formula \[\left| a \right| = a\] for any real value\[a\].
Next we will talk about modulus of a variable. Suppose, we have a variable \[x\] and what is \[\left| x \right|\] . So, the definition of the modulus of a variable is \[\left| x \right| = \left\{ \begin{array}{l}x;x \ge 0\\ - x;x < 0\end{array} \right.\] . So, this is the main definition of modulus. \[x\] can take any real value like negative or zero or positive value. But the answer will always be positive.
  The sign of the modulus is always positive.

Note: Students become puzzled if they are asked to write a sign of modulus of a positive number. So, the result will be the same in that case. Always remember that the sign of the modulus of a number whatever may be is always positive.