Absolute Value Definition....2

In summary, the absolute value of a number is its distance from 0 on a number line, always represented as a positive value. To find the absolute value, one can use the absolute value symbol or follow specific steps depending on the number's sign. Absolute value and magnitude are often used interchangeably, but they have slightly different meanings. Absolute value is used in various fields, such as mathematics, physics, engineering, and economics, for applications such as determining distance, calculating error, and finding vector components' magnitude. While related, absolute value and modulus are not the same, as modulus represents the remainder after dividing two numbers.
  • #1
mathdad
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Use the algebraic definition of absolute value to rewrite the expression below in a form that does not contain absolute value.

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  • #2
Yes again:)
 

Related to Absolute Value Definition....2

What is the definition of absolute value?

The absolute value of a number is its distance from 0 on a number line. It is always a positive value, so it represents the magnitude or size of a number without regard to its sign (positive or negative).

How do you find the absolute value of a number?

To find the absolute value of a number, you can either use the absolute value symbol (| |) or follow these steps:

  1. If the number is positive, the absolute value is equal to the number itself.
  2. If the number is negative, remove the negative sign to make it positive.
  3. If the number is 0, the absolute value is still 0.

What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but they have slightly different meanings. While absolute value represents the distance from 0 on a number line, magnitude represents the size or amount of something. Magnitude can be positive, negative, or zero, while absolute value is always positive.

What are some real-world applications of absolute value?

Absolute value is used in various fields, including mathematics, physics, engineering, and economics. Some examples of its applications include determining the distance between two points, calculating the error in measurements, and finding the magnitude of a vector's components.

Is absolute value the same as modulus?

While they are related concepts, absolute value and modulus are not exactly the same. Modulus is the remainder after dividing two numbers, while absolute value is the distance from 0 on a number line. However, in some cases, the absolute value and modulus of a number can be the same, such as when the number is positive.

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