Definition:

The absolute value of a number is a measure of its distance from zero on the number line.

Formula:

The absolute value of a number x is denoted by |x| and is defined as:

|x| = x if x is positive|x| = -x if x is negative|x| = 0 if x is zero

Properties:

• Absolute value is always non-negative.
• The absolute value of a sum is less than or equal to the sum of the absolutes.
• The absolute value of a product is equal to the product of the absolutes.
• The absolute value of a quotient is equal to the quotient of the absolutes.

Applications:

• Absolute value is used to find the distance of a number from zero.
• Absolute value is used to find the magnitude of numbers.
• Absolute value is used in calculus to find the distance between points.
• Absolute value is used in mathematics to solve a variety of problems, such as finding the solutions to inequalities.

Examples:

|3| = 3|-5| = 5|0| = 0|-2| = 2

Additional Notes:

• The absolute value of a complex number is not defined.
• The absolute value of a vector is not defined.
• The absolute value of a matrix is not defined.