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Chapter 1: Problem 78

Find each absolute value. SEE EXAMPLE 7. (OBJECTIVE 4). $$|120|$$

Short Answer

Expert verified
The absolute value of 120 is 120.

Step by step solution

01

Absolute value definition

The absolute value of a real number is its distance from zero on the number line. It is always nonnegative.
02

Determining Absolute Value

Given the number is 120, and since it's a positive number, the absolute value of 120 is simply 120 itself.

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Key Concepts

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

Number Line
Imagine the number line as a straight line that stretches infinitely in both directions. It is a visual representation of numbers where each point corresponds to a real number. The number line is a helpful tool because it makes abstract concepts more tangible. It provides a way to understand the position and order of numbers visually.

  • The center point of the number line is zero.
  • To the right of zero are the positive numbers.
  • To the left of zero are the negative numbers.
The position of a number on this line shows its value relative to zero. For example, on a number line:
  • The number 2 is two units from zero on the right side.
  • The number -3 is three units from zero on the left side.
When discussing absolute value, it's important to remember that it refers to the distance from zero, without considering which direction (left or right) you move to get there.
Real Numbers
Real numbers are all the numbers we commonly use and encounter in everyday life. They include many different types of numbers which can be classified into various categories.

  • Natural Numbers: These are the counting numbers like 1, 2, 3, etc.
  • Whole Numbers: This includes all natural numbers along with 0.
  • Integers: These are whole numbers that include negative numbers, such as ..., -3, -2, -1, 0, 1, 2, 3,...
  • Rational Numbers: Numbers that can be expressed as a fraction of two integers, such as \( \frac{1}{2} \), 0.75, or -5.
  • Irrational Numbers: Numbers that cannot be written as simple fractions, such as \( \pi \) or the square root of 2.
In essence, real numbers cover everything on the number line. They form a continuum without any gaps, and the concept of absolute value applies to all these numbers by expressing how far they are from zero.
Nonnegative Numbers
Nonnegative numbers are numbers that are either greater than or equal to zero. They lie on or to the right of zero on the number line. Understanding nonnegative numbers is crucial because absolute values are always nonnegative.

Here are some characteristics and examples of nonnegative numbers:
  • Zero: The starting point on the number line.
  • Positive Numbers: Numbers like 1, 2, 3, and so on.
  • Fractions and Decimals: Nonnegative numbers like 0.5, 1.75, \( \frac{3}{4} \).
Nonnegative numbers also include the absolute value of any real number. For instance, the absolute value of -7 is 7, a positive, nonnegative number. This concept helps in ensuring calculations regarding distance or magnitude, using absolute value, don't result in negative values, reflecting real-world measurements like length or time.

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Most popular questions from this chapter

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