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Chapter 10: Problem 49

Find the absolute value. $$ |-3.625| $$

Short Answer

Expert verified
3.625

Step by step solution

01

- Understand the Definition

The absolute value of a number is its distance from zero on a number line, regardless of direction. It is always a non-negative number.
02

- Identify the Number

The number given in the exercise is -3.625.
03

- Compute the Absolute Value

To find the absolute value of -3.625, convert it to its positive equivalent. This gives us 3.625.
04

- Write the Answer

Thus, the absolute value of -3.625 is 3.625.

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Key Concepts

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

number line
A number line is a visual tool used in mathematics to represent numbers in a straight line. Each point on the line corresponds to a number, allowing us to easily see relationships between them.
The center of the number line is zero. Numbers to the right of zero are positive, and numbers to the left are negative. This helps us understand the concept of absolute value.
For example, we can locate -3.625 on the number line to the left of zero, and 3.625 to the right of zero. By looking at the distances from zero in both directions, we can see that the absolute value is the same because it shows the distance without considering direction.
non-negative number
A non-negative number is any number that is either positive or zero. These numbers are always to the right of zero on the number line.
The absolute value of a number is always non-negative, since it measures distance from zero. Distance cannot be negative!
For instance, the absolute value of -3.625 is 3.625. This conversion shows that although -3.625 is negative, its absolute value is expressed as a non-negative number.
distance from zero
The concept of distance from zero is critical in understanding absolute values. Absolute value reflects how far a number is from zero, without considering the direction (positive or negative).
We can use the number line to visualize this distance. Both -3.625 and 3.625 are 3.625 units away from zero. Therefore, the absolute value of -3.625 is 3.625, as it measures the same distance.
By focusing on distance from zero, we see that absolute values only care about magnitude, not direction. This simplifies many mathematical problems by converting all distances to non-negative values.

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