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Chapter 9: Problem 55

Evaluate each expression. [-10.1]

Short Answer

Expert verified
10.1

Step by step solution

01

Understand Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of direction. For any number, this means ignoring the negative sign if it has one.
02

Apply Absolute Value

Given the number is [-10.1], we apply the absolute value, which removes the negative sign. Hence, [-10.1] becomes [10.1].

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Key Concepts

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

Number Line
Understanding the concept of a number line is essential in grasping absolute values. A number line is a straight, horizontal line with numbers placed at intervals.
The center of the number line is zero, with positive numbers to the right and negative numbers to the left.
Each number's position represents its value. For example, 5 is five units to the right of zero, and -5 is five units to the left of zero.
The number line helps us visually comprehend numerical relationships and perform operations like addition, subtraction, and finding absolute values.
Distance from Zero
The distance from zero on a number line is a crucial concept in understanding absolute values. Regardless of direction, every number on the number line has a distance from zero.
For instance, the distance of 7 from zero is 7 units, and the distance of -7 from zero is also 7 units.
This concept helps in determining the absolute value of a number.
Distance is always positive, so the absolute value of both 7 and -7 is 7, since we only consider how far the number is from zero, not its direction.
Positive and Negative Numbers
Positive and negative numbers represent quantities on either side of zero on the number line. Positive numbers are greater than zero and are found to the right of zero.
Negative numbers are less than zero and are found to the left of zero. When we talk about absolute value, we are interested in the magnitude of these numbers, not their sign.
For example, the absolute value of -10.1 is 10.1 because we remove the negative sign and only consider the distance from zero.
This helps in simplifying expressions and solving problems involving distance or magnitude, where direction does not matter.

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Most popular questions from this chapter

Compared to the graph of \(f(x)=\sqrt{x}\), the graph of \(g(x)=-\frac{1}{2} \sqrt{x}\) is _____ across the \((x\) -axis \(/ y\) -axis \()\) and (stretched / shrunken) by a factor of _______. Some points on the graph of \(f(x)\) are \((0,0),(4,2),\) and (16,4) . Corresponding points on the graph of \(g(x)\) are (0, 0), (4, _____), and (16, ______).

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In order, to see how important properties of operations with real numbers are related to similar properties of composition of functions. Fill in the blanks when appropriate. Consider the following function. $$f(x)=x$$ Choose any function \(g\), and find \((f \circ g)(x)\). Then find \((g \circ f)(x)\). How do the two results compare?
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