Lesson 9.2The Real Number SystemObjective - To classify and identify numbers within the real number system.

Understanding Rational and Irrational

Rational Numbers Irrational Numbers-Any number that can be written as a fraction.

-Non-terminating and non-repeating decimals.

“Makes Sense” “Doesn’t Make Sense”

-can’t be written as a fraction.

237

18

0.49

0.7

fractions

wholes

integers

terminatingdecimalsrepeatingdecimals

71

181

49100

79

3 1.73205...1.212112111211112...

0.123456789101112...

0.15255355545555...

Sets of NumbersNaturals - Natural counting numbers.

{ 1, 2, 3… }

Wholes - Natural counting numbers and zero.{ 0, 1, 2, 3… }

Integers - Positive or negative natural numbers or zero.{ … -3, -2, -1, 0, 1, 2, 3… }

Rationals - Any number which can be written as a fraction.

Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal.

Reals - Rationals and irrationals.

Sets of NumbersReals

Rationals Irrationals- any number thatcan be written as afraction.

2

3, 7, -0.4

Fractions/Decimals Integers

61

4 , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3...

Negative Integers Wholes…-3, -2, -1 0, 1, 2, 3...

Zero0

Naturals1, 2, 3...

- non-terminating and non-repeating decimals

2

This is a Venn Diagram that displays the following sets of numbers: Naturals, Wholes, Integers, Rationals, Irrationals, and Reals.

Naturals1, 2, 3...

Wholes0

Integers-3 -19

Rationals2

3

61

4

-2.65

Irrationals

2

Reals

Sets of Numbers

Identify each number below as natural, whole,integer, rational, irrational, or real. More than onemay apply.

71) 8

2) 0

3) 24

4) 6

5) 8

Rational , Real

Whole, Integer, Rational , Real

Integer, Rational , Real

Irrational , Real

,Whole, Integer, Rational , RealNatural

Identify each number below as natural, whole,integer, rational, irrational, or real. More than onemay apply.

46) 5

7) 9

8) 16

9) 25

10) 8

Rational , Real

Integer, Rational , Real

,Whole, Integer, Rational , RealNatural

Integer, Rational , Real

Irrational , Real

Graph on Number Line

• (Hint: turn them all into decimals)

2 1 10, , 8,

3 5 3

0.6,0.2,2.9,3.3

-1 0 1 2 3 4 5 6

Order From Least to Greatest

58, 4, , 3.75

2

58 2.9, 4, 2.5, 3.75

2

-4 -3 -2 -1 0 1 2 3 4 5 6 75

4, 3.75, , 82

Compare Using < > or =

• Turn them both either to:– Fractions and use the heart method – Decimals and compare place values

Use <, >, or = to compare.

41) 0.69

52) 0.658

53) 0.59

3 14) 10 3

=

<

>

<

20.6

3

0.6 0.6

0.625 0.65

5 5

9 10

Homework

Page 455 (12-46) even

• Write the title

• Write the number and question

• Show work

• Highlight answer