Understanding the Absolute Value of Numbers and its Mathematical Applications

absolute value

The absolute value of a number is the non-negative value of the number, regardless of its sign

The absolute value of a number is the non-negative value of the number, regardless of its sign. In simpler terms, it is the distance of a number from zero on the number line. It is denoted by two vertical bars (| |) surrounding the number.

For example, the absolute value of 5 is 5, since 5 is 5 units away from 0 on the number line. Similarly, the absolute value of -5 is also 5, as it is 5 units away from 0 in the opposite direction.

In mathematical notation, the absolute value of a number is determined by the following formula:

|a| =
a, if a ≥ 0
-a, if a < 0 This means that for positive numbers or zero, the absolute value is equal to the number itself. But for negative numbers, the absolute value is equal to the number with the sign flipped, resulting in a positive value. Absolute value is commonly used in various mathematical operations such as finding the distance between two numbers, solving equations involving inequalities, and evaluating the magnitude of a quantity without considering its direction.

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