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Chapter 3: Problem 355

In the following exercises, locate and label the integer on the number line. $$ -3 $$

Short Answer

Expert verified
-3 is located three units to the left of zero on the number line.

Step by step solution

01

Understand the Number Line

A number line is a straight line with numbers placed at equal intervals along its length. Positive numbers are located to the right of zero, and negative numbers are located to the left of zero.
02

Identify the Position of -3

-3 is a negative integer, so it should be located to the left of zero on the number line.
03

Locate -3 on the Number Line

Starting at zero, move three units to the left to locate -3. Mark this position on the number line.
04

Label the Point

Label the marked point with -3 to complete the exercise.

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Key Concepts

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

Integers
Integers are a set of whole numbers that include both positive numbers, negative numbers, and zero. They do not have fractional or decimal parts. For example:
  • Positive integers: 1, 2, 3, ...
  • Negative integers: -1, -2, -3, ...
  • Zero: 0
Understanding integers is fundamental in math as they represent distinct points on the number line. Each integer has a unique position.
Negative Numbers
Negative numbers are integers less than zero. They are represented with a minus sign (-) in front of them. On a number line, negative numbers are always found to the left of zero. For instance, -1, -2, and -3 are all negative numbers. Here's how to understand negative numbers better:
  • Negative numbers decrease in value as you move further to the left on the number line.
  • -3 is three units to the left of zero, while -1 is one unit to the left of zero.
Recognizing negative numbers is important when performing operations such as addition and subtraction.
Locating Points
Locating and labeling points on the number line is an essential skill in mathematics. Here is a straightforward way to do this:
  • Start at zero, the center point of the number line.
  • Identify the direction needed: move to the right for positive numbers and to the left for negative numbers.
  • Count the units to reach the desired number and mark the point.
For the exercise with -3, you'd start at zero, then move three units to the left to find and label the point -3. This visual way of understanding numbers helps in various mathematical concepts.

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