6 Questions
2 Views

# Real Numbers: Rational and Irrational Numbers

Created by
@WorthyMandelbrot

### What is the definition of a rational number?

A rational number is a real number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.

π, e, √2, or √3

### What is the result of the sum of a rational number and an irrational number?

The sum is always irrational.

### What is the result of the product of a rational number and an irrational number?

<p>The product is always irrational.</p> Signup and view all the answers

### What is the set of rational numbers denoted by?

<p>Q</p> Signup and view all the answers

### What is the set of irrational numbers denoted by?

<p>Q' (or sometimes by R\Q)</p> Signup and view all the answers

## Study Notes

### Rational Numbers

• A rational number is a real number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
• Examples: 3/4, 22/7, 1/2
• Rational numbers can be expressed as finite decimals or recurring decimals.
• Rational numbers are either terminating or repeating.
• The set of rational numbers is denoted by Q.

### Irrational Numbers

• An irrational number is a real number that cannot be expressed as the ratio of two integers, i.e., it is not a rational number.
• Examples: π, e, √2, √3
• Irrational numbers have infinite non-repeating decimals.
• Irrational numbers are non-terminating and non-repeating.
• The set of irrational numbers is denoted by Q' (or sometimes by R\Q).

### Key Properties

• The sum of two rational numbers is always rational.
• The sum of a rational number and an irrational number is always irrational.
• The product of two rational numbers is always rational.
• The product of a rational number and an irrational number is always irrational.
• The set of real numbers is the union of the set of rational numbers and the set of irrational numbers.

## Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

## Description

Test your understanding of real numbers, including rational and irrational numbers, their properties, and examples. Learn about the differences between these two types of numbers and how to identify them.

## More Quizzes Like This

60 questions
12 questions
24 questions
Use Quizgecko on...
Browser
Information:
Success:
Error: