In order to work with algebra, we need to use numbers. Any number that can be used to represent something, such as a distance, a length, or a price, is known as a real number.

The set of real numbers is actually made up of several different groups or sets of numbers.

Here’s a game called the “Universe of Real Numbers.” We’ll use it to learn about the different sets of numbers contained in the set of real numbers.

Each level of the universe has one or more parts labeled with the name of a number group.

Each part of the universe has a list of numbers. Choose numbers in each list that match the number group of that part.

If you correctly match the numbers in a level, you will be transported to the next level. The goal is to make it to the home planet. Now let’s begin.

Now let's continue with today's lesson.

Sets of related numbers can be represented with a Venn diagram.

Here we have a Venn diagram representing the sets of numbers that make up the set of real numbers.

Which of the following sets of numbers is completely contained by the set of whole numbers? Click the "Submit" button after selecting your answer.

The two main divisions of the set of real numbers are the sets of rational and irrational numbers.

We’ll talk more about irrational numbers in a later lesson. Now, let’s take a closer look at rational numbers.

Here we have some rational numbers graphed on a number line.

An integer is a type of rational number.

Which of the numbers shown on the number line is a negative integer? Click the "Submit" button after entering your answer.

The set of integers consists of 0, and all positive and negative numbers without fractional parts.

Each positive integer can be paired with a negative integer. These integer pairs are known as opposites. In this example, -1 and 1 are opposites.

A particular type of integer is known as a whole number.

Which of the numbers shown on the number line is a whole number that is not a positive number? Click the "Submit" button after entering your answer.

The set of whole numbers is made up of the positive integers and 0.

A type of whole number is known as a natural number.

Which of the numbers shown on the number line is a natural number? Click the "Submit" button after entering your answer.

The set of natural numbers is made up of positive integers.

Integers only make up part of the set of rational numbers.

In general, a rational number can be expressed as the ratio of two integers, <EQUATION>, where <EQUATION>.

Sometimes this ratio produces another integer. Here we have: <EQUATION>

Sometimes it produces a number with a fractional part. Here we have: <EQUATION>

Which of the numbers shown on the number line is produced by the ratio <EQUATION>? Click the “Submit” button after entering your answer.

It is important to understand that we can always find another rational number between two distinct rational numbers.

This is stated by the density property for rational numbers.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education