Problem 71 - Elementary and Intermediate Algebra

Question

Find each absolute value. $$|0|$$

Step-by-Step Solution

Answer

|0| = 0

Step 1: Understanding Absolute Value

The absolute value of a number is the distance of the number from 0 on the number line, regardless of its direction. This distance is always non-negative.

Step 2: Identify the Given Number

The given number for this exercise is 0.

Step 3: Calculate the Absolute Value

To find the absolute value of 0, determine the distance of 0 from 0 on the number line. Since 0 is at position 0, the distance is 0.

Step 4: State the Result

The absolute value of 0 is 0.

Key Concepts

Number Line

The number line is a visual representation of numbers placed on a straight line. Each point on the line corresponds to a number. This concept is crucial for understanding absolute values.
For example:

• Positive numbers are placed to the right of 0.
• Negative numbers are placed to the left of 0.

The position of a number on this line helps us easily determine distances and relationships between different numbers.

Distance from Zero

Distance from zero is a key aspect of absolute values. It measures how far a number is from 0, regardless of direction. This distance is always taken as a positive value.
For instance, whether a number is -3 or 3, both have an absolute value of 3 because they are both 3 units away from zero on the number line. This concept helps us treat numbers in a consistent, non-negative manner when discussing their 'absolute' measure.

Non-Negative Values

Non-negative values are numbers that are either positive or zero. This includes all numbers from 0 onwards.
Absolute values are always presented as non-negative. Even if the original number was negative, its absolute value will be non-negative. For example:

• Absolute value of -5 is \(|-5| = 5\).
• Absolute value of 7 is \(|7| = 7\).

Understanding this ensures clarity when dealing with various mathematical problems involving distances and measurements.