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Chapter 1: Problem 14

Find each absolute value. $$ |13| $$

Short Answer

Expert verified
13

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is the distance between that number and zero on the number line, regardless of direction. It's always a non-negative number.
02

Identify the Given Value

The given value to find the absolute value of is 13.
03

Evaluate the Absolute Value

Since 13 is a positive number, its absolute value is 13. This is because the distance from 13 to 0 on the number line is 13 units.

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Key Concepts

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

Number Line
A number line is a visual representation of numbers placed at equal intervals along a straight line. Imagine a ruler where every point represents a number. The center of this line is called zero.
Numbers to the right of zero are positive, and numbers to the left are negative.
Positive numbers represent quantities greater than zero, while negative numbers represent quantities less than zero.
For example, on a number line:
  • 3 is to the right of zero
  • -3 is to the left of zero
Using a number line helps us understand concepts like absolute value, as we can visually measure distances between numbers and zero.
Non-negative Number
A non-negative number is any number that is zero or greater. Simply put, it's a number that is not negative.
Non-negative numbers include zero and all positive numbers. Examples are 0, 1, 2, 3, 4, and so on.
In contrast, negative numbers like -1, -2, -3, etc., are not considered non-negative. The absolute value of a number is always a non-negative number.
This is because it represents a distance, and distances can't be negative. For instance, the absolute value of -5 is 5, which is a non-negative number.
Distance from Zero
The term 'distance from zero' refers to how far a number is from zero on the number line, without considering direction.
Whether the number is to the left or right of zero, we only look at how far it is.
This is what we call its absolute value. For example, both -7 and 7 are 7 units away from zero. Thus, their absolute values are both 7.
The concept of 'distance from zero' simplifies understanding of absolute values, emphasizing that they are always non-negative.

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Most popular questions from this chapter

Use set-builder notation to write each set. The set of all multiples of 5 between 7 and 79

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -8.7,-3,0, \frac{2}{3}, \sqrt{7}, 6 $$

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. $$ (r-s)^{2}-3(2 r-s), \text { for } r=11 \text { and } s=3 $$

Tico's scores on four tests are \(83,91\) \(78,\) and \(81 .\) How many points above his current average must Tico score on the next test in order to raise his average 2 points?

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. \([5(r+s)]^{2},\) for \(r=1\) and \(s=2\)
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