Problem 24 - Fundamentals of Mathematics

Question

Determine each of the values. $$ |0| $$

Step-by-Step Solution

Answer

The absolute value of zero is 0.

Step 1: 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 number.

Step 2: Applying Absolute Value to Zero

The absolute value symbol, denoted by vertical bars \(|\), means we take the distance of a number to zero. Here, we have \(|0|\). Since zero is neither positive nor negative, its distance to zero is zero itself.

Step 3: Final Evaluation

Thus, the absolute value of zero is calculated as \(|0| = 0\).

Key Concepts

Number Line

Imagine the number line as a ruler stretching infinitely in both directions, with zero sitting right in the middle to divide the positive and negative numbers.

• On this number line, every number has a unique position.
• Positive numbers sit to the right of zero. Negative numbers sit to the left of zero.
• The absolute value signifies the "distance" from zero without considering direction.

Zero isn't positive or negative; it's where everything starts. Knowing how to "read" the number line helps understand how absolute value, which measures distance from zero, applies.

Distance from Zero

The concept of distance from zero is central to understanding absolute value.

• Think of absolute value as a "distance" measure without considering direction.
• Distances are always non-negative; they can never be a negative number.

When determining \( |0| \), note that zero has zero distance from itself on the number line, resulting in an absolute value of zero. If you were asked for the absolute value of another number, say \( |-3| \), you'd calculate it as the positive distance, which is 3.

Non-negative Number

A non-negative number is any number that is zero or more.

• This includes all positive numbers and zero.
• Negative numbers are excluded since they fall below zero.

When we talk about absolute value, it always results in a non-negative measurement. This is because we are measuring distance, and distance cannot be negative. Hence, \( |0| = 0 \) is a non-negative result, as zero fits within the non-negative definition.