How do I rewrite expressions using absolute value?

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In summary, absolute value is a mathematical concept that gives the distance of a number from zero on a number line. It is calculated by removing any negative sign in front of the number and has properties such as always being positive, being commutative, and not being affected by multiplication or division. It has numerous real-life applications, such as in physics, mathematics, and economics, and is also commonly used in computer programming for various purposes.
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mathdad
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The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| 1 - sqrt{2} | + 1

The value 1 - sqrt{2} is less than 0.

So, we have -(1 - sqrt{2}) + 1.

-1 + sqrt{2} + 1

Answer: sqrt{2}

Correct?
 
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  • #2
Yes, this is correct.
 

Related to How do I rewrite expressions using absolute value?

What is absolute value?

Absolute value is a mathematical concept that gives the distance of a number from zero on a number line. It is always expressed as a positive value and is denoted by vertical bars around the number.

How is absolute value calculated?

Absolute value is calculated by removing any negative sign in front of the number, if there is one. If the number is already positive, then the absolute value is equal to the original number.

What are the properties of absolute value?

The main properties of absolute value are: it is always positive, it is commutative, it is not affected by multiplication or division, and it follows the triangle inequality.

What are some real-life applications of absolute value?

Absolute value has several real-life applications, such as calculating distance in physics, finding the magnitude of a vector in mathematics, determining the error in measurements, and solving absolute value equations in economics and finance.

How is absolute value used in computer programming?

In computer programming, absolute value is used to find the distance between two points, to sort data in ascending or descending order, to calculate error margins, and to handle negative numbers in algorithms and functions.

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