Problem 46 Find the absolute value. $$ ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 46

Find the absolute value. $$ |0| $$

Short Answer

Expert verified

The absolute value of 0 is 0.

Step by step solution

Understanding Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. It is always non-negative.

Identify the Number

Here, the number provided is 0. We need to find the absolute value of 0.

Calculate Absolute Value

Since absolute value measures the distance from 0 and 0 is at the starting point, the absolute value of 0 is 0.

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Key Concepts

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

distance on number line

Understanding the distance on a number line is essential to grasp the concept of absolute value. The number line is a visual representation where numbers are placed in a straight line, increasing as you move to the right and decreasing as you move to the left. Each point on this line corresponds to a number.
Distance on the number line is measured by counting the number of units between two points. It does not matter which direction you move; the distance is always counted as a positive value.
For example, the distance between -3 and 3 is 6 units because you count 3 to get from -3 to 0 and another 3 to get from 0 to 3, making the total distance 6 units.

non-negative values

Non-negative values include all positive numbers and zero. It means they are either greater than or equal to zero and never negative.
This idea is crucial for understanding absolute values because the absolute value of a number is always non-negative. Think of it as the actual 'size' of the number, disregarding whether it is positive or negative.
For instance, whether you take the absolute value of 7 or -7, the result is always 7 because it is -7 units away from zero, and we don't use negative distances.

absolute value calculation

Calculating absolute value involves finding how far a number is from zero on the number line, and it is always non-negative. It is represented as $|a|$ where $'a'$ is any number.
If 'a' is positive, then $|a| = a$. If 'a' is negative, then $|a| = -a$ because the distance cannot be negative.
For example, the absolute value of -5 is calculated as follows:

Identify that -5 is negative.
Remove the negative sign to get the distance: -(-5) becomes 5.

Therefore, $|-5| = 5|$. Similarly, $|3| = 3$ because 3 is already positive.

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91影视

Find the absolute value. $$ |0| $$

Short Answer

Step by step solution

Understanding Absolute Value

Identify the Number

Calculate Absolute Value

Key Concepts

distance on number line

non-negative values

absolute value calculation

One App. One Place for Learning.

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