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Chapter 8: Problem 62

Simplify. $$ |0| $$

Short Answer

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Step by step solution

01

Understand Absolute Value

The absolute value of a number refers to its distance from zero on the number line, regardless of its sign. It is always a non-negative number. The absolute value is denoted by two vertical bars, like this: \( |x| \).
02

Apply Absolute Value to Zero

To find the absolute value of zero, analyze the distance of zero from itself on the number line. Since zero is at the origin, the distance is 0. Therefore, the absolute value of zero is still 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
A number line is a straight, horizontal line that visually represents numbers in their increasing or decreasing order. Imagine it as a ruler, where zero is the center point, also known as the origin.
  • Positive numbers are placed to the right of zero.
  • Negative numbers are located to the left of zero.
Using a number line helps us see how numbers relate to each other, making concepts like addition, subtraction, and absolute value more intuitive. When we talk about the "absolute value" on a number line, we are referring to how far a number is from the zero, regardless of the direction (left or right). This directionless measurement is essential for calculating distances and understanding number relationships.
Non-Negative Number
A non-negative number is a number that is either positive or zero. These numbers are always greater than or equal to zero, never negative.
  • Examples include numbers like 0, 2, 16, or any other positive decimal or fractional form.
  • Zero is the smallest non-negative number because it is neither positive nor negative.
In mathematics, absolute values are always non-negative because they measure the distance from zero without considering direction. Hence, no matter if a number is negative or positive, its absolute value will always return a non-negative result.
Distance from Zero
The term "distance from zero" describes how far a number is from zero on the number line. This distance is always a non-negative value, as it does not consider the number's direction.
  • For example, the distance from zero to 5 is 5 units, and the distance from zero to -5 is also 5 units.
  • This is why the absolute value of a number is always equal to its distance from zero, shown by the notation \(|x|\).
When evaluating the absolute value of zero itself, it remains zero because there is no distance between zero and itself. Understanding "distance from zero" helps clarify the concept of absolute value and its non-negative nature.

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Most popular questions from this chapter

Solve. See the Concept Check in this section. Choose the type of variation that each equation represents. a Direct variation b. Inverse variation c. Joint variation $$ y=\frac{2}{3} x $$

Solve. At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see. Round to the nearest tenth of a mile.

Solve. The number of cars manufactured on an assembly line at a General Motors plant varies jointly as the number of workers and the time they work. If 200 workers can produce 60 cars in 2 hours, find how many cars 240 workers should be able to make in 3 hours.

Complete the following table for the inverse variation \(y=\frac{k}{x}\) over each given value of \(k .\) Plot the points on a rectangular coordinate system. $$ \begin{array}{c|c|c|c|c|c|} \hline x & {\frac{1}{4}} & {\frac{1}{2}} & {1} & {2} & {4} \\ \hline y {=\frac{k}{x}} & {} & {} & {} & {} \\ \hline \end{array} $$ $$ k=1 $$

For each statement, find the constant of variation and the variation equation. See Examples 5 and 6 \(y\) varies directly as the square root of \(x ; y=0.4\) when \(x=4\)
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