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Absolute Value Definition

In mathematics, the absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a number, disregarding its sign. The absolute value is denoted by vertical bars or pipes surrounding the number. For example, the absolute value of -5 is written as |-5| and equals 5.

Absolute value number line

Since “5” is 5 units away from zero, the absolute value of 5 is 5.

Since “-5” is also 5 units away from zero, the absolute value of -5 is also 5.

Absolute value (modulus) of a number is the non-negative value of x without regard to its sign.

Absolute value is denoted as |x|.

\vert x \vert = \begin{cases}
x &\text{if x ≥ 0} \\
-x &\text{if x < 0} \end{cases}

Examples of Absolute Value

|-8| = 8: The absolute value of -8 is 8, as it represents the distance of -8 from zero on the number line.

|3| = 3: The absolute value of 3 is 3 since 3 is already a positive number.

|-2.5| = 2.5: The absolute value of -2.5 is 2.5, indicating its magnitude without considering its negative sign.

|0| = 0: The absolute value of 0 is 0, as it lies exactly on the origin.

Conclusion

The absolute value of a number provides a measure of magnitude, disregarding its sign. Its significance extends across multiple disciplines, including mathematics, physics, and data analysis. Understanding the concept of absolute value is essential for solving equations, inequalities, and optimization problems. By grasping its applications, you gain a powerful tool to analyze data, quantify errors, and make informed decisions. Embrace the versatility of the absolute value and unlock its potential in your mathematical and scientific endeavors.

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