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Chapter 1: Problem 21

Find each absolute value. $$ |-4.21| $$

Short Answer

Expert verified
The absolute value of -4.21 is 4.21.

Step by step solution

01

Understand Absolute Value

Absolute value refers to the distance of a number from zero on the number line, regardless of direction. It is always a non-negative number.
02

Identify the Given Number

The number given in the exercise is -4.21.
03

Apply the Absolute Value Definition

To find the absolute value, take the magnitude of -4.21, which means ignoring the negative sign.
04

Result

The absolute value of -4.21 is 4.21.

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Key Concepts

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

Distance from Zero
The concept of absolute value is closely related to the idea of distance from zero. When we talk about distance in everyday life, we always think in non-negative terms. For example, if you say a store is 2 miles away, it doesn鈥檛 matter in which direction you go鈥攏orth, south, east, or west鈥攊t鈥檚 still a distance of 2 miles. Similarly, the absolute value of a number is the distance of that number from zero on the number line. This distance is always non-negative, regardless of whether the number is positive or negative. For instance, the absolute value of -4.21 is 4.21, which tells us that -4.21 is 4.21 units away from zero on the number line.
Number Line
A number line is a visual representation of numbers laid out in a straight line. It helps us understand the position and distance of numbers relative to zero. The center of the number line is zero. Numbers to the right of zero are positive, and numbers to the left are negative. When we denote the absolute value of a number, we're essentially asking, 'How far is this number from zero?' For positive numbers, their absolute value is the number itself because they are already at a distance from zero. For negative numbers, we ignore the negative sign to determine the distance. For example, -4.21 on the number line is 4.21 units to the left of zero. Thus, its absolute value is 4.21.
Magnitude
Magnitude refers to the size or length of something, without considering its direction. In terms of numbers, magnitude is how large a number is without taking into account whether it's positive or negative. When determining the absolute value, we are essentially finding the magnitude of a number. For example, -4.21 and 4.21 have the same magnitude because they are the same distance from zero, but in opposite directions. The absolute value strips away the direction (negative sign) and leaves us with just the magnitude. Hence, \(-4.21\)'s magnitude is 4.21.

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Most popular questions from this chapter

Write an equivalent expression using a commutative law. Answers may vary. $$ -9(a b) $$

Explain in your own words why \(7 / 0\) is undefined.

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 4.3 \notin \mathbb{Z} $$

Use roster notation to write each set. The set of all natural numbers that are multiples of 10

Divide. $$ \left(-\frac{2}{7}\right) \div(-1) $$
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