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Chapter 1: Problem 88

Graph the given set on a number line. $$\\{1,4,5,8\\}$$

Short Answer

Expert verified
Place points at 1, 4, 5, and 8 on the number line.

Step by step solution

01

- Identify each point

Identify each of the numbers in the set: 1, 4, 5, and 8.
02

- Draw the number line

Draw a horizontal line and label it with appropriate units to accommodate all numbers in the set. For this example, the number line should cover at least from 0 to 9.
03

- Mark each number on the number line

Place a dot or a point above each number you identified in Step 1: 1, 4, 5, and 8.
04

- Double-check placements

Verify that each point is correctly placed according to its numerical value on the number line.

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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 simple yet powerful tool used to visualize numbers and mathematical concepts. It鈥檚 essentially a straight, horizontal line marked at regular intervals, where each point corresponds to a number.

To draw a number line, follow these steps:
  • Start by drawing a horizontal line.
  • Choose a range that includes all the numbers you need. For example, if you're plotting numbers from 1 to 8, your number line might run from 0 to 9.
  • Mark equal intervals along the line. These intervals represent whole numbers, but you can also include fractions or decimals if needed.
A correctly drawn number line helps you see relationships between numbers easily. It is a fundamental tool for various mathematical operations like addition, subtraction, and even understanding inequalities. When plotting points, be precise to ensure accurate representation and interpretation.
Set Notation
Set notation is a mathematical shorthand to describe a collection of objects, typically numbers. A set is usually denoted by curly brackets { }, and the numbers or elements inside are separated by commas. For example, the set {1, 4, 5, 8} contains the numbers 1, 4, 5, and 8.

Here are a few key points to remember about set notation:
  • Distinct elements: Each number or element in a set is unique.
  • Order doesn鈥檛 matter: {1, 4, 5, 8} is the same as {4, 1, 8, 5}.
  • Finite vs. Infinite: Sets can be finite (with a specific number of elements) or infinite.
Understanding set notation is essential for graphing on a number line. By clearly defining what numbers you need to plot, you make the process more straightforward and error-free.
Plotting Points
Plotting points on a number line is an excellent way to visually represent a set of numbers. It's like adding specific landmarks to a map, helping you see each number's location and relationship to others.

Follow these steps to plot points:
  • Identify the numbers: Start by noting each number you need to plot. In this example, the numbers are 1, 4, 5, and 8.
  • Locate the points: On your number line, find the position of each number.
  • Mark the points: Use a small dot or another marker to indicate where each number is on the line.
Double-check your work by ensuring each dot is correctly placed. This confirmation step is crucial for avoiding mistakes and ensuring accurate representation. Properly plotted points help clarify concepts in various math topics, from simple arithmetic to advanced algebra.

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Most popular questions from this chapter

Sketch the given set on a number line. $$\\{x |-3 \leq x \leq 2\\}$$

We know that multiplication means repeated addition. That is, 4 times 3 means add 3 four times. In view of this and the rule for adding negative integers, what should 4 times \(-3\) be equal to?

Evaluate the given expression. Remember to follow the order of operations. $$\frac{12+6 \cdot 3}{6+3 \cdot 3}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.28(56)-0.36(63)$$

Evaluate the given expression. Remember to follow the order of operations. $$32+16 \div 8-6$$
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