Question

Write the absolute values of the following integers:
\[ + 13,{\text{ }} - 31,{\text{ }}10,{\text{ }} - 42,{\text{ }}0,{\text{ }} + 60,{\text{ }} - 17,{\text{ }}26,{\text{ }} - 21\]

Answer 1

Hint: The absolute value is also the modulus of the number. The absolute value of a number is the non-negative value of the number. The absolute value or modulus of a real number \[x\] is denoted as\[\left| x \right|\], which is the non-negative value of \[x\] without regard to its sign. If \[x\] is a positive number then \[\left| x \right| = x\] and so\[\left| { - x} \right| = x\].

Complete answer: We are given with the following integers:
\[ + 13,{\text{ }} - 31,{\text{ }}10,{\text{ }} - 42,{\text{ }}0,{\text{ }} + 60,{\text{ }} - 17,{\text{ }}26,{\text{ }} - 21\]
We have to find its absolute value or modulus of these numbers.
For any real number x absolute value is defined as the actual numerical value of the numbers. Here we have integers and as integers are also real numbers so it will obey the rule of modulus or absolute value.
For any real number \[x\left( {positive} \right)\] and \[ - x\left( {negative} \right)\] , the absolute value is \[\left| x \right| = x\]and\[\left| { - x} \right| = x\].
From the above statement of absolute value we have the following absolute values of the integers:

i.\[ + 13\]
The absolute value of \[ + 13\] is \[\left| { + 13} \right| = 13\]

ii.\[ - 31\]
The absolute value of \[ - 31\] is \[\left| { - 31} \right| = 31\]

iii.\[10\]
The absolute value of \[10\] is \[\left| {10 = 10} \right|\]

iv.\[ - 42\]
The absolute value of \[ - 42\] is \[\left| { - 42} \right| = 42\]

v.\[0\]
The absolute value of \[0\] is \[\left| 0 \right| = 0\]

vi.\[ + 60\]
The absolute value of \[ + 60\] is \[\left| { + 60 = 60} \right|\]

vii.\[ - 17\]
The absolute value of \[ - 17\] is \[\left| { - 17} \right| = 17\]

viii.\[26\]
The absolute value of \[26\] is \[\left| {26} \right| = 26\]

ix.\[ - 21\]
The absolute value of \[ - 21\] is \[\left| { - 21} \right| = 21\]

Note:
The absolute value of a number is considered as the numerical distance of that number from \[0\]in the number line irrespective of its sign. The term ‘module’ was introduced by Jean-Robert Argand in 1806 which means unit of measurement in French. The absolute value or modulus function is used to represent the positive square roots of real numbers.