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Chapter 1: Problem 41

Explain why \(|-4|=4\).

Short Answer

Expert verified
The absolute value indicates distance from zero, so |鈭�4| is 4

Step by step solution

01

Define Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number.
02

Apply the Definition

For the number -4, its distance from zero on the number line is 4. Hence, |鈭�4| = 4.

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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 line that visually represents numbers in sequence.
It extends infinitely in both directions with zero positioned at the center.
Positive numbers are placed to the right of zero, and negative numbers are placed to the left.
Each number has a unique position on the number line.
By using a number line, it's easy to visualize and compare the size of different numbers.
When we talk about the position of a number on this line, we're referring to its numerical value.
Non-Negative Number
A non-negative number is any number that is zero or greater.
This means non-negative numbers include all positive numbers and zero.
Negative numbers do not fall into this category.
Absolute values are always non-negative because they represent a distance, which can't be negative.
For example, the absolute value of both -4 and 4 is 4, which is a non-negative number. This is because distance, regardless of direction, is always a non-negative quantity.
Distance from Zero
Distance from zero refers to how far a number is from zero on the number line.
This distance is measured in units and is always a non-negative number.
Regardless of whether the original number is positive or negative, its distance from zero is its absolute value.
For instance, the number -4 is 4 units away from zero.
Thus, \(-4\text){absolutevalue}=4\).
This helps explain why the absolute value of -4 is 4.
Since the concept of distance doesn't change direction, it ensures the absolute value is always non-negative.

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Most popular questions from this chapter

Problem: The length of a rectangle is \(3 \mathrm{~cm}\). Its width is \(8 \mathrm{~cm}\). Find its area. $$ \text { Incorrect Answer: } \begin{aligned} A &=L W \\ A &=3 \cdot 8 \\ A &=24 \end{aligned} $$

The formula \(P=\left(\frac{w}{w+i}\right) 100\) represents the relationship of the percent of X-rays absorbed by an antiscatter grid \(P\), the width of each grid strip \(w\), and the width between the grid strips \(i\). If the width of each grid strip is 50 micrometers and the width between the grid strips is 350 micrometers, find the percent of X-rays absorbed. Round to the nearest percent.

The sales tax rate in a state is \(6 \%\). Find the sales tax on a purchase of \(\$ 750\).

The International Basketball Federation rules (2006) state, "For all men's competitions in all categories, the circumference of the ball shall be no less than \(749 \mathrm{~mm}\) and no more than \(780 \mathrm{~mm}\) (size 7)." Find the maximum volume of the ball in cubic millimeters. Round to the nearest whole number. (Source: www.fiba.com)

\(\sqrt{-49}\)
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