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When we talk about absolute value, we are referring to the distance of a number from zero on the number line. This value is always positive because distance can't be negative. For example, whether you look at \(-3\) or \(+3\), both are 3 units away from zero, so their absolute value is 3. The same concept applies when dealing with decimal numbers. \(-3.5\) and 3.5 are both 3.5 units away from zero, meaning \(|-3.5|\) = 3.5.
Understanding this helps us simplify problems where we compare numbers based on their absolute values, treating all numbers as positive for the sake of distance calculation.

After finding the absolute values of two numbers, the next step is to compare these values to determine which is smaller or larger. For the numbers given in the exercise: \(-3.5\) and \(-4.5\). We first find \(|-3.5|\) = 3.5 and \(|-4.5|\) = 4.5.
Now, we simply compare these positive values. We see that 3.5 is less than 4.5. This means that the distance of \(-3.5\) from zero is less compared to the distance of \(-4.5\) from zero. Thus, in absolute terms, we can clearly state that \|-3.5\| is less than \|-4.5\|.
This comparison allows us to make judgments about the sizes of negative numbers treated as positive distances.

In the context of absolute values and comparison, transforming all numbers to their positive equivalents makes it much easier to compare them directly. This conversion removes any confusion caused by negative signs. Thus, working with positive values simplifies many mathematical problems, especially in exercises involving absolute values.
For example, when we consider \(|-3.5| \text{ and } |-4.5|\), we treat them as positive numbers for comparison: 3.5 and 4.5. This straightforward approach lets us easily determine that 3.5 is smaller than 4.5, meaning \(-3.5\) is the lesser number in this context.

• Always convert to absolute (positive) values first.
• Then compare the numbers directly.
• Select the number corresponding to the smaller absolute value.

Using these steps ensures accuracy and simplicity in solving comparison problems involving absolute values.