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Chapter 3: Problem 98

Find the absolute value: \(|-13.4|\) (Section \(1.3,\) Example 8 )

Short Answer

Expert verified
The absolute value of \(-13.4\) is \(13.4\).

Step by step solution

01

Define Absolute Value

The absolute value of a number \(a\), denoted as \(|a|\), represents the distance of \(a\) from zero on the number line, irrespective of the direction. Therefore, the absolute value of a number is always positive or zero.
02

Apply the Absolute Value

For the given number \(-13.4\), the absolute value is the number itself without its negative sign. This is because absolute value is concerned with the magnitude of the number disregarding its direction (negative or positive). So, \(|-13.4|\) is equal to \(13.4\).

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Key Concepts

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

Understanding the Number Line
The number line is a visual representation of all real numbers laid out in a straight line. This line is infinite in both directions, extending from negative to positive values.
The central point of the number line is zero, marking the separation between negative and positive numbers.
  • To the left of zero are the negative numbers.
  • To the right, you'll find the positive numbers.
A number's absolute position on this line is its distance from zero, irrespective of whether it's a negative or positive number.
By observing a number's location on the line, we can easily understand its magnitude.
Measuring Distance from Zero
Distance from zero on a number line is what defines the concept of absolute value. It shows how far a number is from zero, without considering direction. For instance, take the number \(-13.4\).
Although it's negative, its distance from zero is quantified by removing the negative sign.
  • This distance is always represented as a non-negative number.
  • By ignoring the direction, we focus purely on magnitude.
This approach helps understand numbers' true size without negative or positive bias. Whether a number is on the left or right, its distance from zero stays the same.
Positive or Zero Values
When calculating absolute value, we end up with a positive number or zero because of its definition. Since absolute value represents a distance, it can never be negative. For \(-13.4\), the direction is disregarded, leading to a result of \(13.4\).
This principle applies to all numbers, providing consistency:
  • If a number is positive, its absolute value remains the same.
  • If a number is negative, the absolute value is its positive counterpart.
  • The absolute value of zero is, logically, zero.
This ensures that absolute values are straightforward and easy to grasp, simplifying the understanding of a number's real-world magnitude.

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Most popular questions from this chapter

Make Sense? In Exercises \(70-73\), determine whether each statement "makes sense" or "does not make sense" and explair your reasoning. The slope-intercept form of a line's equation makes it possible for me to determine immediately the slope and the \(y\) -intercept.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I use \(y=m x+b\) to write equations of lines passing through two points when neither contains the \(y\) -intercept.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line through \((3,1)\) and \((3,-5)\) has zero slope.

Will help you prepare for the material covered in the next section. From \((0,-3),\) move 4 units up and 1 unit to the right. What point do you obtain?

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((4,-7)\) and perpendicular to the line whose equation is \(x-2 y=3\)
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