Problem 49 - Algebra 1

Question

Evaluate the expression. (Review 2.1 ) $$|1.07|$$

Step-by-Step Solution

Answer

The absolute value of 1.07 is 1.07.

Step 1 - Identify the number

The number to find the absolute value for is 1.07.

Step 2 - Apply the absolute value function

The absolute value of a number is the number itself if it is positive, and its opposite if it is negative. Since 1.07 is positive, the absolute value of 1.07 is 1.07.

Key Concepts

Evaluating Expressions

Understanding how to evaluate expressions is a cornerstone of algebra. It involves finding the value of a mathematical phrase by following a series of operations. In our case, the expression is the absolute value of 1.07, expressed as \(|1.07|\). The primary step is to recognize any special operators or functions within the expression. Here, the absolute value symbol \(| |\) indicates that we are looking for the magnitude of the number, ignoring its sign.

For students, getting the hang of evaluation means practicing with different types of operators and expressions. A helpful tip is to always perform operations within parentheses or special functions, like the absolute value, before dealing with other arithmetic operations that may be part of the expression. This is often referred to as the 'order of operations' in mathematics.

Absolute Value Function

The absolute value function is a fundamental concept in mathematics, sometimes causing confusion among students. At its core, the absolute value of a number refers to the distance of that number from zero on the number line, regardless of direction. Thus, it is always a non-negative value.

When you see the absolute value symbol, which are the vertical bars as in \(|1.07|\), you are to interpret that as the command, 'Give me the distance of this number from zero.' In the case of positive numbers, the absolute value does not change the number because they are already at a positive distance from zero. However, for negative numbers, the absolute value returns the equivalent positive number. For instance, the absolute value of -1.07 would be 1.07.

Positive Numbers

Positive numbers are all the numbers greater than zero that we often encounter in everyday contexts, such as counting objects, measuring length, or determining how much something costs. They are an integral part of the number system and are represented on the right side of zero on the number line.

In the context of the absolute value function, positive numbers play a simple but crucial role. They remain unchanged since their distance from zero is already a positive measure. When evaluating expressions with the absolute value function, recognizing whether a number is positive can immediately simplify the process, as with the number 1.07 in our exercise. It’s helpful for students to think of the absolute value function as a question asking 'how far?', and if already on the positive side, the answer is direct and straightforward.