Question

Evaluate the expression.$|0|$

Short answer

The evaluation of the expression $|0|$ is 0.

Step-by-step solution

Understanding the Absolute Value Concept

The absolute value of a number is the number's distance from zero on the number line. It removes any negative sign in front of a number, which makes all numbers positive, except for zero. In the case of zero, the absolute value is 0 itself because zero is not positive or negative.

Apply the Absolute Value to Zero

We apply the concept to 0. So, $|0|$ equals 0.

Key concepts

Understanding Algebra

Algebra is a fascinating area of mathematics where we use letters, often referred to as variables, to represent numbers. It’s like a code where instead of using actual numbers each time, one has the flexibility to use these variables to stand for the numbers that might change or might not even be known at the moment.

This concept is incredibly powerful because it allows us to create formulas and equations that can solve a vast array of problems. At the heart of algebra is the understanding of expressions and operations – adding, subtracting, multiplying, and dividing – among these variables and numbers. Algebra is a building block for more advanced topics in mathematics and essential for various real-world applications such as engineering, science, economics, and much more.

When dealing with expressions, such as the absolute value of zero, representing it as $|0|$, algebra allows us to apply defined rules and concepts to uncover the values these expressions hold, no matter the complexity.

The Significance of the Number Line

The number line is a basic yet incredibly insightful tool used in various branches of mathematics. It's a straight, horizontal line that extends infinitely in both directions, with a starting point typically at zero, known as the origin. Numbers to the right of zero are positive, and those to the left are negative, visually representing the concept of positive and negative numbers.

To use the number line effectively, imagine each point on the line corresponds to a real number, and the distance between points on the line represents the difference between these numbers. When we talk about absolute value, we are referring to the distance a number is from zero on this line, regardless of which direction the number lies from zero. Therefore, on a number line, both -5 and +5 are five units away from zero, which is why they both have an absolute value of 5.

Positive and Negative Numbers

Positive and negative numbers are essential in understanding the foundations of mathematics. Positive numbers are all the numbers greater than zero and are often represented without a plus sign, while negative numbers are less than zero and are denoted by a minus sign in front of them.

• Positive numbers indicate a quantity that is more than nothing (zero).
• Negative numbers represent a deficiency or loss, such as debt.
• Zero is the neutral number that is neither positive nor negative.
• When we take the absolute value of a negative number, we're essentially looking for its positive counterpart.

In the exercise $|0|$, zero serves as a unique case because it's at the exact middle point between the positive and negative realms of the number line. This reflects life in a sense! We often think in terms of gains and losses, but zero reminds us that there is a starting point which is neither – a balance point. Absolute value, therefore, allows us to objectively measure distance or quantity without taking into account which side of zero it falls on.