The absolute value of a number, a, expressed as ∣a∣, is the non-negative value of a. Therefore, the absolute value of a negative number changes its sign whereas the absolute value of a non-negative number is equal to the number itself. ∣-3∣=3∣3∣=3 A compact way to write the absolute value of a real number is by using a curly bracket. ∣a∣={a-aif a≥0if a<0 The absolute value of a number a can be thought of as the distance between a and 0 on the number line. Since the absolute value of -3 and 3 are equal, these numbers are also the same distance from 0.
There are several properties and identities that can be useful when simplifying expressions or solving equations including absolute values. For real values of a and b, these relationships are true.