/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Determine each value. $$ |9|... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 37

Determine each value. $$ |9| $$

Short Answer

Expert verified
The absolute value of 9 is 9.

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on a number line, without considering direction. Absolute value is always non-negative.
02

Evaluate the Absolute Value

To find the absolute value of any number, simply remove any negative sign that might be in front of the number. For a positive number, the absolute value is the number itself.
03

Apply the Concept

Given the number is 9, which is already positive, its absolute value is the same. Therefore, the absolute value of 9 is 9.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Positive Numbers
In mathematics, positive numbers are numbers greater than zero. They can appear with or without a "+" sign, but by default, they are assumed to be positive if no sign is shown. Positive numbers are primarily used to represent quantities with physical meaning, like length, time, money, and more. They are located to the right of zero on a number line.
  • For example, if you have 5 apples, this can be expressed with the positive number 5.
  • Positive numbers add up in straightforward ways; for instance, 2 + 3 equals 5.
Understanding positive numbers is key when dealing with absolute values because the concept involves turning any number into its non-negative counterpart. For positive numbers, this means they remain unchanged when their absolute value is considered.
Number Line
A number line is a straight, horizontal line that visually represents numbers as points along its length. The center point of a number line is zero, and numbers are evenly spaced on either side. It is a simple yet powerful tool to understand numerical concepts.
  • To the right of zero, numbers increase in positive magnitude (1, 2, 3, ...).
  • To the left of zero, numbers decrease and are negative (-1, -2, -3, ...).
Using a number line helps in seeing why the absolute value of a number is its distance from zero. When we say that the absolute value of 9 is 9, it鈥檚 because 9 units separate the number 9 from zero on this line. The direction doesn't matter, only the distance.
Distance from Zero
Distance from zero is a concept tied to absolute value. It measures how far a number is from zero on a number line, ignoring its direction. This is why absolute values are always non-negative. Even if you're dealing with negative numbers, like -5, its distance from zero is a positive one (5 units away).
  • To find the distance from zero: treat both positive and negative numbers in the same way. They both end up as the same non-negative absolute value.
  • This also shows how absolute values are useful in real-world problems. Picture negative temperatures where conduction usually involves positive numbers for easier computation.
In mathematical operations, knowing the distance from zero helps in comparisons, calculations, and understanding the overall magnitude of numbers without worrying about which side of zero they are on.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For the following 4 problems, perform the indica ted operations The low temperature today in Denver was \(-4^{\circ} \mathrm{F}\) and the high was \(-42^{\circ} \mathrm{F}\). What is the temperature difference?

Find each value. (-14)\(\cdot(-3)\)

Use the order of operations to simplify \(\left(5^{2}+3^{2}+2\right) \div 2^{2}\).

How should each number be read? $$ -(-1) $$

Find the value of each of the following. Use a calculator to check each result. $$ -4-(-1) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.