Problem 15 Find each absolute value. $$ ... [FREE SOLUTION]

91影视

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 1: Problem 15

Find each absolute value. $$ |-46.8| $$

Short Answer

Expert verified

46.8

Step by step solution

Understand Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of whether the number is positive or negative. Essentially, it is the non-negative value of the number.

Identify the Value Inside the Absolute Value Notation

Here the number inside the absolute value notation is `-46.8`.

Calculate the Absolute Value

Since absolute value denotes distance from zero and is always non-negative, the absolute value of `-46.8` is simply `46.8`. Therefore, $|-46.8| = 46.8$.

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Key Concepts

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

Number Line

To understand absolute value, let's first revisit the concept of the number line. A number line is a straight line that has numbers placed at equal intervals along its length. The center of the number line is zero. Positive numbers are found to the right of zero, while negative numbers are to the left. For instance, -5 is to the left of zero, and 5 is to the right.

Absolute value shows how far a number is from zero on the number line. So, for -46.8, you first look at its position on the number line. No matter if the number is positive or negative, its distance from zero is what counts. This leads us to our next topic, non-negative value.

Non-Negative Value

Whenever we talk about absolute value, we mean the non-negative value of a number. That means whether our number is negative or positive, we ignore its sign. For example, the number -46.8 becomes 46.8 when we take its absolute value. This is because absolute value measures only how far a number is from zero鈥攊gnoring if it's left or right on the number line.

This concept emphasizes that distances cannot be negative. Distances are always measured in non-negative values. Therefore, no matter how negative a number may be, its absolute value will always be positive or zero.

Distance from Zero

Finally, let鈥檚 delve into the idea of distance from zero. This is the crux of understanding absolute value. Imagine you are standing at zero on the number line. The distance to any number is measured by how many steps you take. If the number is -46.8, you would travel 46.8 steps to the left. However, when measuring distance, the direction of travel doesn't matter鈥攐nly the number of steps.

Thus, the absolute value of -46.8 is just 46.8 because distance is always a non-negative number. This applies to all numbers, which means the distance from zero helps us understand that absolute value is always non-negative.

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91影视

Find each absolute value. $$ |-46.8| $$

Short Answer

Step by step solution

Understand Absolute Value

Identify the Value Inside the Absolute Value Notation

Calculate the Absolute Value

Key Concepts

Number Line

Non-Negative Value

Distance from Zero

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