/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 298 In the following exercises, list... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 298

In the following exercises, list the (a) whole numbers, (b) integers, \(\odot\) rational numbers, \(@\) irrational numbers, \(\Theta\) real numbers for each set of numbers. $$ -9,-3 \frac{4}{9},-\sqrt{9}, 0.4 \overline{09}, \frac{11}{6}, 7 $$

Short Answer

Expert verified
Whole numbers: 7 Integers: -9, -3, 7 Rational numbers: -9, - 3 \frac{4}{9}, -\frac{3}{3}, 0.4 \bar{09}, \frac{11}{6}, 7 Irrational numbers: None Real numbers: -9, - 3 \frac{4}{9}, -\frac{3}{3}, 0.4 \bar{09}, \frac{11}{6}, 7

Step by step solution

01

Identify the whole numbers

Whole numbers are non-negative integers including zero. Look at the set and pick the numbers that fit this definition.
02

Identify the integers

Integers include all whole numbers and their negative counterparts. Select numbers from the set that are whole numbers or negative whole numbers.
03

Identify the rational numbers

Rational numbers can be expressed as a fraction of two integers (where the denominator is not zero). Determine which numbers in the set can be written as a fraction.
04

Identify the irrational numbers

Irrational numbers cannot be written as a simple fraction. They have non-repeating, non-terminating decimal expansions. Pick any numbers that fit this definition.
05

Identify the real numbers

Real numbers include all rational and irrational numbers. List all numbers from the set under this category.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Whole Numbers
Whole numbers are fundamental in mathematics. They include all positive numbers and zero, without decimals or fractions. In simpler terms, whole numbers are like counting numbers but with zero added.
Examples of whole numbers are 0, 1, 2, 3, 4, and so on. Because whole numbers can't be negative, numbers like -1 or -2 are not considered whole numbers.
So, from the given set, the whole number is just 7.
Exploring Integers
Integers include both positive and negative whole numbers, along with zero. They do not have fractions or decimals.
For example, numbers like -3, 0, 4, and -10 are all integers. This means any number you can count with or against without a fraction is an integer.
So, from the given set \(-9, -\frac{4}{9}, -\text{sqrt}(9), 0.4 \overline{09}, \frac{11}{6}, 7\), the integers are -9 and 7.
Diving into Rational Numbers
Rational numbers are numbers that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b eq 0\).
Rational numbers can be positive, negative, whole numbers, and even fractions and decimals as long as they can be written as a fraction.
Some examples include \(\frac{1}{2}\), -3, and 0.25. So from our given set, the rational numbers include \(-3\frac{4}{9}, -\text{sqrt}(9), 0.4 \overline{09}, \frac{11}{6}, 7\). In this context -\text{sqrt}(9)= -3.
Unraveling Irrational Numbers
Irrational numbers are the numbers that cannot be written as simple fractions. Their decimal expansions are non-repeating and non-terminating.
Examples of irrational numbers include \( \frac{\text{pi}}{} \), \(\text{sqrt}(2)\), and \(0.10110111011110...\).
From the set provided \(-9,-3\frac{4}{9},-\text{sqrt}(9), 0.4 \backslash overline{09}, \frac{11}{6}, 7\), none of the numbers fit into the irrational category.
Understanding Real Numbers
Real numbers encompass both rational and irrational numbers. Essentially, any number that exists on the number line is a real number.
This includes whole numbers, integers, rational numbers, and irrational numbers.
So from our initial set, all the numbers \(-9, -3\frac{4}{9}, -\text{sqrt}(9), 0.4 \overline{09}, \frac{11}{6}, 7\), all fall under the category of real numbers.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{0}{u-4.99}, \text { where } u \neq 4.99 $$

In the following exercises, simplify. $$ \left(\frac{5}{16} n-\frac{3}{7}\right) \div 0, \text { where } \frac{5}{16} n-\frac{3}{7} \neq 0 $$

In the following exercises, write each decimal as a fraction. $$ 1.464 $$

In the following exercises, simplify. $$ 12\left(\frac{5}{6} p\right) $$

In the following exercises, list the (a) whole numbers, (b) integers, \(\odot\) rational numbers, \(@\) irrational numbers, \(\Theta\) real numbers for each set of numbers. $$ -8,0,1.95286 \ldots, \frac{12}{5}, \sqrt{36}, 9 $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.