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Chapter 1: Problem 63

Find each absolute value. $$|-58|$$

Short Answer

Expert verified
58

Step by step solution

01

Understand Absolute Value Definition

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

Identify the Number Inside the Absolute Value

The number in question is (-58).
03

Apply the Absolute Value

Since absolute value measures distance and ignores direction, the absolute value of (-58) is simply 58.

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Key Concepts

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

Distance from Zero
Understanding the distance from zero is key to mastering absolute values. Absolute value measures how far a number is from zero on a number line.
Distance is always a positive measure because it considers only the magnitude, not direction. For instance, the distance from -58 to 0 is 58, and the distance from 58 to 0 is also 58.
This helps to explain why the absolute value of -58 is 58. It's about how far a number is from zero, not about whether it's on the left or right side of zero.
Non-Negative
The term 'non-negative' can be confusing, but it simply means 'not negative.' All absolute values are non-negative.
When we calculate the absolute value, we only care about the distance, which ensures that the result can never be negative.
Consider the number line example again. Whether dealing with positive numbers (like 58) or negative numbers (like -58), the absolute value is the distance from zero, which is always a positive number or zero.
So, you can confidently say that \(|-58| = 58\), and it's non-negative.
Number Line
A number line is an essential tool for visualizing absolute value. Imagine a line with zero in the center. Positive numbers are to the right, and negative numbers are to the left.
To find the absolute value, you start at zero and measure how many steps it takes to reach the given number. You don't worry about the direction.
For example, to find \(|-58|\) on the number line, count 58 steps from zero towards -58.
Since we're only interested in the distance, \(|-58|\) equals 58, ignoring the direction entirely.
Practicing with a number line can make understanding absolute value much simpler.

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Most popular questions from this chapter

A gambler loses a wager and then loses "double or nothing" (meaning the gambler owes twice as much) twice more. After the three losses, the gambler's assets are \(-\$ 20 .\) Explain how much the gambler originally bet and how the \(\$ 20\) debt occurred.

Write an equivalent expression without using grouping symbols. $$ -(3 x+5) $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ |13.5+8(-4.7)|^{3} $$

Brianna insists that if you can add real numbers, then you can also subtract real numbers. Do you agree? Why or why not?

List in order from least to greatest. $$-\frac{2}{3}, \frac{1}{2},-\frac{3}{4},-\frac{5}{6}, \frac{3}{8}, \frac{1}{6}$$
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