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Chapter 1: Problem 104

Simplify. $$ |-0.75| $$

Short Answer

Expert verified
The simplified absolute value of \\(-0.75\\) is \\(0.75\\).

Step by step solution

01

Understanding Absolute Value

The absolute value of a number refers to its distance from zero on the number line, regardless of its direction. Thus, the absolute value of any real number is always non-negative.
02

Identifying the Number

In this exercise, the number given is \(-0.75\). We know that it is a negative number since it is less than zero.
03

Applying the Absolute Value

The absolute value function removes the negative sign from a number. So, when we take the absolute value of \(-0.75\), we get \(0.75\).

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Key Concepts

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

Understanding the Number Line
The number line is a visual representation where numbers are placed in order from left to right. It helps us understand the position and relationship between different numbers.

The number line is centered at zero, with positive numbers to the right and negative numbers to the left.
  • Every point on the line corresponds to a real number.
  • Zero is the central point, acting as a neutral boundary.
  • Distances between points are uniform, making comparisons straightforward.
When working with absolute values, we are interested in the distance of a number from zero, often measured as a positive quantity regardless of the number's sign.
Exploring Negative Numbers
Negative numbers are values less than zero, typically found to the left on a number line. They can represent various concepts like debt, temperature below freezing, or depth below sea level.

Some key characteristics of negative numbers include:
  • They are opposite to positive numbers regarding signs and positions on the number line.
  • Adding two negative numbers results in a larger negative number.
  • The product of two negative numbers is positive.
Negative numbers can sometimes appear intimidating, but their rules are consistent. When using absolute values, the focus shifts from the sign to the magnitude of these numbers.
Performing Mathematical Operations
Mathematical operations involve processes like addition, subtraction, multiplication, and division, allowing us to manipulate numbers and solve problems effectively.

In the context of absolute values, the main operation performed is removing the sign of a negative number to find its magnitude:
  • Addition: Combine values, keeping in mind their signs.
  • Subtraction: Find the difference, often rearranging as addition of opposites.
  • Multiplication: Multiply numbers, remembering the sign rules.
  • Division: Divide values, also following sign conventions.
Understanding these basic operations is crucial for solving more complex mathematical problems and working confidently with numbers in varied contexts.

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