/*! 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 105 Describe the difference between ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 105

Describe the difference between a rational number and an irrational number.

Short Answer

Expert verified
Rational numbers can be expressed as a ratio or fraction of two integers, whereas irrational numbers cannot be expressed as a ratio of two numbers and aren't exact fractions. Rational numbers either terminate or repeat in decimal form, while irrational numbers do not; their decimal expansions go on forever without repeating.

Step by step solution

01

Describe Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction \( p/q \) of two integers, with the denominator \( q \) not equal to zero. Since integers are also rational, we might say that a rational number is a number which can be represented in a ratio form.
02

Describe Irrational Numbers

Irrational numbers cannot be expressed as a ratio between two numbers and it is not an exact fraction. In other words, they cannot be written as \( p/q \) with \( p \) and \( q \) as integers and \( q \) not equal to zero. They are usually the result of non-repeating, non-terminating decimals.
03

Differentiate Between the Two

The fundamental difference between rational and irrational numbers is that rational numbers can be expressed as a fraction with integers in both the numerator and the denominator while irrational numbers cannot be expressed in such a way. Sometimes another main difference is that while rational numbers either terminate or repeat in decimal form, irrational numbers do neither; their decimal expansions continue without repeating indefinitely.

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!

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 Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The product of \(-9\) and \(-3,\) decreased by \(-2\)

Will help you prepare for the material covered in the next section. In each exercise, a subtraction is expressed as addition of an opposite. Find this sum, indicated by a question mark. $$7-10=7+(-10)=?$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I saved money by buying a computer for \(\frac{3}{2}\) of its original price.

In each exercise, determine whether the given number is a solution of the equation. $$4 x+2=3(x-6)+8 ;-11$$

Insert parentheses in each expression so that the resulting value is 45 $$2 \cdot 5-\frac{1}{2} \cdot 10 \cdot 9$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.