/*! 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 6 Classify each number as one or m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(700,000,000,000\) (The federal 2008 bailout fund in dollars)

Short Answer

Expert verified
The number is a natural number, integer, rational number, and real number.

Step by step solution

01

Identify as a Natural Number

Natural numbers are all positive integers starting from 1, including counting numbers. Since \(700,000,000,000\) is a positive whole number with no decimal or fractional part, it qualifies as a natural number.
02

Identify as an Integer

Integers include all whole numbers, both positive and negative, including zero. \(700,000,000,000\) is a whole number, hence it is an integer.
03

Identify as a Rational Number

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since \(700,000,000,000\) can be represented as \(\frac{700,000,000,000}{1}\), it is a rational number.
04

Identify as a Real Number

Real numbers include all rational and irrational numbers. Since \(700,000,000,000\) is a rational number, it is also a real number.

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.

Natural Numbers
Natural numbers are often introduced to students as the counting numbers that start from 1, and go upwards. They are simple and straightforward as they include numbers like 1, 2, 3, and so on.
  • These numbers do not include zero.
  • They are always positive, meaning that they do not incorporate negative numbers or fractions.
  • Natural numbers are used in everyday counting and ordering, such as counting apples or steps.
In our exercise, the number \(700,000,000,000\) fits neatly into the natural numbers category. It is a massive jackpot among natural numbers but still fundamentally the same kind of number as 1 or 2, but on a much larger scale. Recognizing such large figures as natural numbers helps in understanding that natural numbers span an infinite range.
Integers
Integers expand upon natural numbers by including zero and negative numbers. They encompass:
  • All positive numbers, turning natural numbers into a subset.
  • All negative numbers without any fractional or decimal parts.
  • Zero, making them symmetric around it.
The number \(700,000,000,000\) is indeed an integer because it is a whole number with no fractional component. The concept of integers is incredibly useful because it allows us to perform operations like subtraction across a broad spectrum of problems, incorporating the aspect of positivity and negativity. For example, if you were borrowing money, integers comfortably express both the gain and debt.
Rational Numbers
Rational numbers take the form of fractions or ratios, where both the numerator and the denominator are integers, and the denominator is not zero.
  • They can represent whole numbers, fractions, and repeating or terminating decimals.
  • Numbers like \(\frac{1}{2}\) and \(\frac{450}{3}\) are classic examples.
  • All integers can be expressed as rational numbers by giving them a denominator of 1.
With this understanding, \(700,000,000,000\), when expressed as \(\frac{700,000,000,000}{1}\), fits perfectly into the rational numbers category. Thus, rational numbers have a fantastic ability to bridge the gap between integers and fractions, offering a versatile approach to number representation.
Real Numbers
Real numbers are like an all-inclusive club. They include every possible kind of number you can think of in the realm of numbers that you typically deal with in school or daily life.
  • They include both rational and irrational numbers.
  • Every number on the number line is a real number.
  • Irrational numbers, such as \(\pi\) and \(\sqrt{2}\), are also part of the real numbers.
Since \(700,000,000,000\) is a rational number, it automatically qualifies as a real number as well. Real numbers allow for a comprehensive understanding of mathematics because they form the basis for algebra, calculus, and beyond. They provide a complete picture for any numeric task undertaken in real-world applications, from computing areas to statistics.

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

The table lists the average tuition and fees (in constant 2010 dollars) at public colleges and universities for selected years. $$\begin{array}{|l|l|l|l|l|l|}\hline \text { Year } & 1980 & 1990 & 2000 & 2005 & 2010 \\\\\hline \begin{array}{l}\text { Tuition and Fees } \\\\\text { (in 2010 dollars) }\end{array} & 5938 & 7699 & 9390 & 11,386 & 13,297 \\\\\hline\end{array}$$ (a) Find the equation of the least-squares regression line that models the data. (b) Graph the data and the regression line in the same viewing window. (c) Estimate tuition and fees in 2007 . (d) Use the model to predict tuition and fees in 2016 .

Given an equation having \(x\) and \(y\) as variables, explain how to determine the \(x\) - and \(y\) -intercepts.

Sketch by hand the graph of the line passing through the given point and having the given slope. Label Through \((-2,-3), m=-\frac{3}{4}\)

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(4,1),(3,-5),(-2,3),(3,7)\\}$$

The table lists the worldwide average household spending (in dollars) on Apple products for selected years. $$\begin{array}{|l|c|c|c|c|} \hline \text { Year } & 2009 & 2011 & 2013 & 2015 \\\ \hline \begin{array}{c} \text { Spending } \\ \text { (\$ dollars) } \end{array} & 62 & 158 & 265 & 444 \end{array}$$ (a) Use regression to find a formula \(f(x)=a x+b\) so that \(f\) models the data. (b) Interpret the slope of the graph of \(y=f(x)\) (c) Estimate the average household spending on Apple products in 2014 and compare it with the actual value of \(\$ 343\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.