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### Real Number System

- Important subsets of the real numbers are: the natural numbers, the whole numbers, the integers, the rationals, and the irrationals.
- The number line can be used to graph sets of numbers.
- Each positive number has 2 square roots. The positive one is called the principal square root.
- Use decimal approximations of irrational numbers to compare and order a set of real numbers that includes some irrationals.

### Real Number System

To what sets of numbers does the following number belong?

- 8

- 8

Real, Integer, Rational

To what sets of numbers does the following number belong?

− [22/60]

− [22/60]

Real, Rational

To what sets of numbers does the following number belong?

√5

√5

Real, Irrational

Order the numbers from largest to smallest value:

π, [28/9] , 3.5 , √{10}

π, [28/9] , 3.5 , √{10}

[28/9] , π, √{10} , 3.5

To what sets of numbers does the following number belong?

- 2

- 2

real, integer, rational

To what sets of numbers does the following number belong?

[5/15]

[5/15]

real, rational

To what sets of numbers does the following number belong?

√{50}

√{50}

real, irrational

To what sets of numbers does the following number belong?

- 67

- 67

real, rational, integer

To what sets of numbers does the following number belong?

− [1/8]

− [1/8]

real, rational

To what sets of numbers does the following number belong?

√{100}

√{100}

real, irrational

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Real Number System

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Real Number System
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Cannot Divide by Zero
- Decimals
- Example: Terminating or Repeating
- Real Number System, Cont.
- Real Number System, Cont.
- Example 1: Which Set of Numbers
- Example 2: Graph on Number Line
- Example 3: Approximate Irrational Number
- Example 4: Order Largest to Smallest

- Intro 0:00
- Real Number System 0:31
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Cannot Divide by Zero
- Decimals
- Example: Terminating or Repeating
- Real Number System, Cont. 3:37
- Square Roots
- Examples
- Irrational Numbers
- Examples
- Perfect Square
- Real Number System, Cont. 6:49
- Example: Number Line
- Example 1: Which Set of Numbers 7:54
- Example 2: Graph on Number Line 10:04
- Example 3: Approximate Irrational Number 12:47
- Example 4: Order Largest to Smallest 13:57

1 answer

Last reply by: Dr Carleen Eaton

Wed Jan 14, 2015 11:50 PM

Post by Harlan Reece on December 30, 2014

How did you arrive at 3.1459 as the repeated pattern of Pi?

1 answer

Last reply by: Dr Carleen Eaton

Sat Sep 14, 2013 2:35 PM

Post by Prince Dalieh on August 6, 2013

In the lecture,you said that irrational numbers can not be express as A/B an example of irrational number is Pi,and Pi is 22/7 or 3.14.

My question is is 22/7 is rational or irrational and does it in the form of A/B or not?

2 answers

Last reply by: Taylor Wright

Mon Jun 17, 2013 11:36 PM

Post by Taylor Wright on June 17, 2013

How did you approximate it to 1.73 ? Is there a specific method for figuring this out?