Objective - To recognize, graph, and compare rational numbers.

Rational Number - any number that can be written

as a fraction.3ie : 7

1, 53

ie : 0.9including decimals...9

10 , 2.31 312

100

ie : 0.4including decimalsthat repeat...

49

, 5.17 17599

ie : 5including Integers...51

, 62 621

ie : 13including Wholes... 131

, 0 02

Rational Numbers

Fractions/Decimals Integers

2.5 1, 35

3,7

, 0.45 …-3, -2, -1, 0, 1, 2, 3…

Negative Integers

…-3, -2, -1

Wholes

0, 1, 2, 3...

Zero

0

Naturals

1, 2, 3...

Create a Venn Diagram that shows the relationshipsbetween the following sets of numbers.

Naturals, Wholes, Integers, Rationals

Naturals1, 2, 3...

Wholes0

Integers-3-47

Rationals

2.5

135

37

0.45

Identify all of the sets to which each number belongs. (Naturals, Wholes, Integers, Rationals)

1) -6

2)

578

3) 14

4) 0.8

Integer

Rational

Natural

Rational

, Rational

, Whole, Integer, Rational

1) 0

2) - 2.03

3)

4)

Whole

Rational

Rational

Rational

215

0.8

Identify all of the sets to which each number belongs. (Naturals, Wholes, Integers, Rationals)

, Integer, Rational

Show that each number below is Rational by writing

it as a fraction in the form a , where b 0.b

1) 17

32) 54

3) 0.89

4) 0.4

5) 8

6) 2.33

7) 1.5

8) 6

171

234

89100

49

81

332100

5110

112

61

233100

Comparing Rational Numbers in Decimal Form

Use < or > to compare.

1) 8.45987 8.51 8.459878.51

<

2) 0.3 0.335 0.33333...0.335

<

3) 14.2 1.538 14.2 1.538

>0

Use < or > to compare the fractions below.

1) 4

5 5

7

2) 3

11 1

3

3) 5

8 9

16

4) 5

12 4

9

35 35 28 25

>

33 33 9 11

<

16 16 10 9

>

36 36 15 16

<

77 5

5

33 11

11

22 1

1

33 4

4

Comparing Rational Numbers in Fraction Form

Graph the fractions below on a number line, then order them from least to greatest.

75

, 35

, 13, 1

9

11

2 1 1

2 0 1

2 1 11

2

1

3, 1

9, 3

5, 7

5

13

19

35

75

Graphing Rational Numbers on a Number Line

Graph the following numbers on a number line.

3

112

53

0.4 3.21

-4 -3 -2 -1 0 1 2 3 4

3 112

0.4 53

3.21

4Which is greater 0.58 or ?7

0.58 7 4.00000000 5

3550

7

4910

1

73

47

028

4

2014

2

6056

8

4035

5

5049

7

0.571428>1

0.58

All rational numbers eitherterminate or repeat when

changed to a decimal.

DensityRational numbers are infinitely dense.This implies that between any two rational numbers, an infinite number of other rationalnumbers exist.

0 112

14

18

116

132164