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Chapter 2: Problem 47

Find each of the following absolute values. $$|8|$$

Short Answer

Expert verified
The absolute value of 8 is 8.

Step by step solution

01

Understanding Absolute Value

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

Identify the Absolute Value of 8

Given the number 8, we need to find its absolute value. Since 8 is a positive number, its absolute value is the number itself.
03

Final Answer

The absolute value of 8 is 8 because the distance of 8 from zero is 8 units.

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Key Concepts

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

Exploring the Number Line
The number line is a visual representation where every point corresponds to a real number. Imagine it as an infinite straight line stretching in both directions.
On this line, numbers to the right of zero are positive, while those to the left are negative. Zero sits right in the center.
A helpful way to visualize numbers and their absolute values:
  • Each point on the line marks a specific number.
  • The space between points is equal, representing consistent increments of 1 unit.
  • Positive numbers extend to the right of zero.
  • Negative numbers extend to the left of zero.
  • The number line helps in quickly determining the absolute value by observing how far a number is from zero, regardless of direction.
Understanding the number line is fundamental in grasping the concept of absolute value and aids in visualizing distances effectively.
Understanding Positive Numbers
Positive numbers are values greater than zero, appearing on the right side of the number line. They give us a sense of quantifiable addition or increase in value.
Here鈥檚 what to remember about positive numbers:
  • They are represented without a plus sign (+) as the sign is implied.
  • Commonly used in everyday contexts like temperature, height, distance, and counting objects.
  • When determining absolute value, if a number is positive, its absolute value is simply the same number.
In our exercise, the number 8 is positive, and therefore, its absolute value remains 8. Understanding and identifying positive numbers is crucial when working with numerical properties like absolute value.
Calculating the Distance from Zero
The absolute value is essential for identifying how far a number is from zero on the number line, regardless of whether it's positive or negative.
This concept highlights:**Distance from Zero**:
  • The absolute value of any number is its distance from zero.
  • It is always non-negative, as it measures a magnitude.
  • No matter the direction on the number line, the focus is solely on how many units away a number is from zero.
  • The notation with vertical bars, such as \( |8| \), signifies this distance.
In our specific example, the distance of 8 from zero is 8 units. Thus, the absolute value \( |8| \) equals 8. Recognizing this distance helps solidly grasp absolute value by showing its reliance on numerical placement, not direction.

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Most popular questions from this chapter

The Bright Angel trail at Grand Canyon National Park ends at Indian Garden, \(3,060\) feet below the trailhead. Write this as a negative number with respect to the trailhead.

At 10: 00 in the morning in White Bear Lake, Minnesota, Zach notices the temperature is 5 degrees below zero Fahrenheit. Write this temperature as a negative number. By noon the temperature has dropped another 10 degrees. What is the temperature at noon?

Yamina is flying from Phoenix to San Francisco on a Boeing 737 jet. When the plane reaches an altitude of \(33,000\) feet, the temperature outside the plane is 61 degrees below zero Fahrenheit. Represent this temperature with a negative number. If the temperature outside the plane gets warmer by 10 degrees, what will the new temperature be?

At 11: 00 in the morning in Superior, Wisconsin, Jim notices the temperature is 15 degrees below zero Fahrenheit. Write this temperature as a negative number. At noon it has warmed up by 8 degrees. What is the temperature at noon?

Perform the indicated operations. $$2(5+8)$$
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