Problem 44 - Prealgebra

Question

Find each of the following absolute values. $$\left|-\frac{1}{10}\right|$$

Step-by-Step Solution

Answer

The absolute value is \(\frac{1}{10}\).

Step 1: Understand Absolute Value

The absolute value of a number is the distance of the number from zero on the number line, without regard to direction. This means that the absolute value of a number is always non-negative.

Step 2: Identify the Number Inside Absolute Value

In this problem, the number inside the absolute value is \(-\frac{1}{10}\).

Step 3: Apply the Absolute Value Rule

Since the absolute value of a number is its distance from zero, we drop the negative sign from \(-\frac{1}{10}\) to find its absolute value. Thus, \(\left|-\frac{1}{10}\right| = \frac{1}{10}\).

Step 4: Conclusion

The absolute value of \(-\frac{1}{10}\) is \(\frac{1}{10}\).

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are placed to the left of 0 on the number line.
When you're dealing with negative numbers, think about them as owing something or a deficit. For example, if you have -3, imagine this as you owe three candies or have a depth in a pit.

• Negative numbers are shown with a minus sign (-) before the number.
• They are crucial in many real-life contexts, such as temperature below zero or debts.
• Negative numbers are less than any positive number or zero.

In our exercise, \(-\frac{1}{10}\) is a negative number. This means it's less than zero, indicating a small deficit or owing of a tenth.

Exploring the Number Line

A number line is a horizontal line that visually represents numbers in a sequential order from left to right.
Zero is typically in the middle, with positive numbers on the right and negative numbers on the left. This simple tool helps us understand numbers by showing their size relative to each other.

• It gives a visual representation of the concept of distance, as each number has a specific position on the line.
• Positive numbers increase to the right of zero, while negative numbers move to the left.
• The number line is endless in both directions, which means there are infinite numbers.

In our exercise, \(-\frac{1}{10}\) would be located slightly to the left of zero, illustrating how it is a negative number.

Distance from Zero

Distance from zero is a concept that simplifies understanding absolute value.
On a number line, any number's distance from zero is viewed without looking at direction, meaning both -3 and 3 are three units away from zero. This is why absolute value is always non-negative.

• Think of absolute value as just the numerical part of a number, ignoring any negative sign.
• This is why the absolute value of \(-\frac{1}{10}\) is \(\frac{1}{10}\), as it's only concerned with the distance or magnitude.
• Distances are always positive, just like how you'd measure the distance from one city to another without considering the direction.

By recognizing this, you can understand why getting rid of the negative sign gives us the absolute value in the exercise.