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Chapter 2: Problem 36

Simplify. $$ |100| $$

Short Answer

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100

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is the distance of that number from zero on a number line, without considering the direction. Thus, the absolute value of any number is always non-negative.
02

Simplify the Expression

Since absolute value is the non-negative value of a number, \(|100| = 100\), because 100 is already a positive number.

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is an important part of understanding the absolute value. In mathematics, simplifying means to make an expression easier to work with or understand by reducing it to its simplest form. When dealing with absolute values, as in the exercise where you have \(|100|\), simplifying the expression ultimately involves recognizing how the absolute value can change, or in this case, actually doesn't change, the number inside the bars.
For absolute value expressions:
  • If the number inside is positive or zero, the absolute value remains unchanged. For instance, \(|100| = 100\).
  • If the number inside is negative, the absolute value turns it positive. If you had \(-100\), then \(|-100| = 100\).
Simplifying is about understanding these basic rules, ensuring that you end up with a non-negative number after evaluating an absolute value.
Number Line
A number line is a visual tool that helps us understand numbers and their absolute values better. It is a straight line where each point represents a number in an increasing order, starting from negative values on the left, through zero, and into positive values on the right.
When discussing absolute value using a number line:
  • The number's absolute value is its distance from zero, regardless of direction.
  • For example, both -100 and 100 are 100 units away from zero.
This visual representation highlights that the absolute value always considers the magnitude, not the direction. It's a valuable method for seeing why results like \(|100| = 100\) make sense.
Non-negative Value
The concept of a non-negative value is intrinsic to understanding absolute values. Non-negative values are numbers that are either positive or zero. They do not include any negative numbers. This concept is especially important in absolute value, as absolute values always result in non-negative numbers, regardless of whether the original number is positive or negative.
In the exercise:
  • When you simplify \(|100|\), you realize 100 is already non-negative, so the expression remains unchanged.
  • If you had \(-5\), it transforms into \(5\) when calculating the absolute value, keeping the end result non-negative.
Understanding non-negative values helps ensure clarity when working with mathematical expressions involving absolute values, ensuring mistakes are minimized while simplifying.

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