Real Numbers (subsets of real numbers and ordering real numbers)

How to use this tutorial!

This tutorial is designed to teach you about Real numbers ( subsets of real numbers and ordering real numbers). The presentation starts with notes and examples followed by practice problems.

This action button when pushed will take you back to the previous slide.

This action button when pushed will advance you to the next slide.

This action button when pushed will take you back to the last slide viewed.

Definitions to know

Natural (or counting) numbers: N= {1,2,3…} Whole numbers: W={0,1,2,3…} Integers: {…-3,-2,-1,0,1,2,3…} Rational numbers: Q={all numbers that can be expressed

in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal.

Irrational number: I={all nonterminating, nonrepeating decimals}. Any number that is not a perfect square has an irrational square root.

Real numbers: R={all rationals and irrationals}

Shortcut

Real Numbers- (R) Irrational Numbers- (I) Rational Numbers- (Q) Integer- (Z) Whole Numbers- (W) Natural Numbers- (N)

Real Numbers

Real numbers can be divided into two basic groups: Irrational numbers and Rational numbers.

Rational Numbers can further be divided into 3 groups: integers, whole numbers, and natural numbers.

N atu ra l N u m b ers(N )

W h o le N u m b ers(W )

In teg ers(Z )

R ation a l N u m b ers(Q )

Irra tion a l N u m b ers(I)

R eal N um bers(R )

Rational Numbers

Rational numbers are all numbers that can be expressed in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal.

A natural number is also always : a whole number, integer, rational number, and real number, etc.

Although a natural number is always an integer; an integer is not always a natural number, etc.

Example: 2, 8/2, 15, 83= real/rational/

integer /whole /natural -2,-8/2,-15,-83= real/rational/

integer

Natural Numbers (N)

Integers (Z)

Whole numbers (W)

Rational numbers (Q)

Irrational Numbers

Irrational numbers are all nonterminating, nonrepeating decimals. Any number that is not a perfect square has an irrational square root.

Examples: 0.078651685…. 1760566….. 17

Examples of Real Number’s Subsets

3/4= real/ rational 0= real/rational/integer/whole .34345646….= real/irrational 1= real/rational/integer/whole/natural = real/irrational 1/3= real/ rational 91,215,225,201,544=

real/rational/integer/whole/natural

Practice 1(subsets of real numbers)

Which of the following numbers is irrational?

A

B

C

D

-1/2

3.63

121

6/55

Practice 2 (subsets of real numbers)

36 is what kind of number?

A

B

C

D

Real/ Irrational

Real/rational/integer/ whole/natural

Real/rational/integer/whole

Real/rational

Practice 3 (subsets of real numbers)

Which of the following is a rational number? A

B

C

D

1/5

3

25/115

Practice 4 (subsets of real numbers)

-6 is what kind of number? A

B

C

D

Real/rational/integer

Real/irrational

Real/rational

Real/rational/integer/ whole

Ordering Real Numbers

Real numbers are ordered from least to greatest.

Example: 1, -4, 49, -16/2, 19/5

ordered from least to greatest would be:

-16/2 (-8), -4, 1, 49 (7), 19/5(3.8)

Practice 5 (ordering real numbers)

Order the following numbers from smallest to largest:

-8, 14/3, 10, 5

A

C

D

B -8, 5, 14/3, 10

-8, 10, 5, 14/3

-8, 14/3, 5, 10

-8, 14/3, 10, 5

Practice 6 (ordering real numbers)

Order the following numbers from least to greatest:

144, -47, 19/6, -13

A

B

C

D

-47, -13, 19/6, 144

-47, -13, 144, 19/6

-13, -47, 144, 19/6

-47, 144, 19/6, -13

References

Information retrieved 11/30/05 from: http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=rational

YAY!!!

You have completed the tutorial on Real numbers (subsets of real numbers and ordering real numbers)!!

Congratulations!!