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Chapter 10: Problem 43

Find the absolute value. $$ |-3| $$

Short Answer

Expert verified
|-3| = 3

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Hence, it's always a non-negative number.
02

Identify the Number

Identify the number inside the absolute value. Here the number is -3.
03

Remove the Negative Sign

Since absolute value measures only the distance from zero, we disregard any negative sign. Hence, the absolute value of -3 is simply 3.

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Key Concepts

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

Number Line
A number line is a visual representation of numbers laid out in a straight line. It helps us easily understand the position of a number in relation to others. All numbers on the line are aligned in increasing order from left to right.

Use this line to see where positive, negative and zero values are. Positive numbers are to the right of zero, and negative numbers are to the left of zero. This visual tool is particularly useful when understanding concepts like absolute value.

For example, on a number line, the number -3 is three units to the left of zero. When we talk about absolute value, we are only interested in how far this number is from zero, not in which direction.
Non-Negative Number
A non-negative number is any number that is either positive or zero. It includes all the numbers that are not negative.

When we calculate the absolute value, we always end up with a non-negative number.

This is because absolute value only measures the distance from zero without considering direction. So, both 3 and -3 would have the same absolute value, which is 3. In other words, the absolute value of any number is never less than zero.
Distance from Zero
Distance from zero is a crucial concept when understanding absolute value. It represents how far a number is from zero on the number line.

This distance is always a positive measure (or zero if the number itself is zero). For example, the distance of -3 from zero is 3 units. Similarly, the distance of 3 from zero is also 3 units.

When we express the absolute value of a number, we're essentially stating this distance. The term 'absolute value' is just another way of asking how far a number is from zero, ignoring any negative signs.

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Most popular questions from this chapter

Divide. $$ \frac{-1.7}{20} $$

Find the mean, median, and mode: 9,17,34,40,40

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Determine the sign of each expression if \(m\) is negative and \(n\) is positive. $$ -\left(\frac{-n}{-m}\right) $$

Multiply. \(-8 \cdot(-1.3) \cdot(-5)\)
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