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Chapter 1: Problem 107

Simplify. $$ |0| $$

Short Answer

Expert verified
The absolute value of 0 is 0.

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value. In this case, we need to evaluate the absolute value of 0.
02

Evaluate |0|

Since 0 is at zero distance from itself, the absolute value of 0 is simply 0.

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Key Concepts

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

Number Line
The number line is a fundamental idea in math that helps us visualize numbers. Imagine a straight line with numbers placed along it at equal intervals. This line stretches infinitely in both directions. Zero is typically placed at the center, serving as a midpoint, with positive numbers to the right and negative numbers to the left.

The number line is an invaluable tool for understanding various mathematical concepts, including absolute values. When determining the absolute value, you can simply think about how far a number is from this central point of zero on the number line, without considering direction.
Distance from Zero
When we talk about the **distance from zero**, we're discussing how many units a number is away from zero on the number line. In math, this is always considered in non-negative terms. This is important because distance is never negative, regardless of direction.

For example, both 3 and -3 are three units away from zero on the number line. Therefore, their absolute values are the same. Understanding this principle simplifies the process of calculating absolute values. The absolute value of 0 is 0 because it is zero units away from itself.
Non-negative Value
In mathematics, a **non-negative value** is a number that's either positive or zero. This means absolute values will always yield a non-negative result because they represent only distance. Negative numbers, when converted to their absolute equivalent, lose their negative sign, upholding the notion of distance.

For instance, the absolute value of -5 is 5 while the absolute value of 5 remains 5. Zero, when considered in terms of absolute value, is straightforward as it is already zero, maintaining its position as a non-negative value. This concept ensures that absolute values can be applied consistently across all real numbers.

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