/*! 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 15 Name the sets of numbers to whic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 15

Name the sets of numbers to which each number belongs. $$ -4.55 $$

Short Answer

Expert verified
-4.55 is a rational number.

Step by step solution

01

Identify the Type of Number

The number given is \(-4.55\). This is a decimal number, not a whole number or integer.
02

Determine if It is a Rational Number

A rational number is any number that can be expressed as the quotient of two integers. Since \(-4.55\) can be expressed as \(-\frac{455}{100}\), it is a rational number.
03

Check Against Other Sets

Now that we know\(-4.55\) is a rational number, it is not a natural number, whole number, or integer because natural numbers and whole numbers are non-negative, and integers do not have a fractional part.

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.

Rational Numbers
Rational numbers are a special group of numbers that can be written as a fraction, where both the numerator and the denominator are integers. The numerator should be an integer, and the denominator cannot be zero. This means any number that fits this form is considered rational.
For example, the number 0.5 is a rational number because it can be written as \( \frac{1}{2} \). Similarly, the number \(-4.55\) is also rational because it can be expressed as \( \frac{-455}{100} \).聽
This shows that rational numbers include integers, fractions, and terminating or repeating decimals. To check if a number is rational, see if you can write it as a simple fraction with integers.
Integers
Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. Essentially, if a number doesn't have a decimal or fractional part, it qualifies as an integer.
Examples of integers include -3, 0, and 7. This set does not include numbers like 0.5 or -4.55 because these have decimal places.
So, remember that while every integer is also a rational number (since it can be expressed as a fraction with a denominator of 1), not every rational number is an integer.
Whole Numbers
Whole numbers are a set of non-negative numbers that include zero and extend to positive numbers without stopping. The most obvious examples of whole numbers are 0, 1, 2, 3, and so on.
Whole numbers do not include fractions, decimals, or negative numbers. Therefore, while numbers like 5 or 0 are whole numbers, \(-4.55\) or even \(-2\) are not considered whole numbers.
Whole numbers are included in the set of integers and, by extension, in the set of rational numbers, because they can be represented as fractions.
Natural Numbers
Natural numbers are often referred to as the counting numbers. They are a part of whole numbers but without zeros. This makes them the set of positive whole numbers such as 1, 2, 3, and so on.
Natural numbers do not include negative numbers, decimals, fractions, or zero. Therefore, numbers like 5 or 102 are natural numbers, whereas \(-4.55\) is not.
Natural numbers are considered a subset of integers, so they are rational numbers as well, because we can represent them with fractions like \( \frac{4}{1} \). However, not every rational number is natural.

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

Define a variable and write an inequality for each problem. Then solve. 9 less than a number is at most that same number divided by 2.

For Exercises \(46-49,\) use the following information. You can use the operators in the LOGIC menu on the TI-83/84 Plus to graph compound and absolute value inequalities. To display the LOGIC menu, press 2nd Test. A graphing calculator can also be used to solve absolute value inequalities. Write the expression you would enter for \(Y 1\) to find the solution set of the inequality \(|2 x-6| > 10 .\) Then use the graphing calculator to find the solution set. (Hint: The absolute value operator is item 1 on the MATH NUM menu.)

Solve each inequality. Then graph the solution set on a number line. \(\frac{1-4 p}{5}<0.2\)

Find the value of each expression. $$ 6(5-8) \div 9+4 $$

Solve each inequality. Graph the solution set on a number line. $$ |-5 y| < 35 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.