Warm UpWarm UpEach square root is between two integers. Name the two integers.

Use a calculator to find each value. Round to the nearest tenth.

10 and 11

3 and 4

1.4

11.1

119

15

2

123

Section 4.7Section 4.7

The Real Number The Real Number SystemSystem

Objective:

In this lesson you’ll:

• Differentiate between rational and irrational numbers. (NS 1.4)

Did you know????Did you know????

Animal

Reptile

Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko.

LizardzzzzzzGecko

Words to Words to know….know….

• Naturals – natural counting numbers { 1, 2, 3, ….}

• Wholes – natural counting numbers and zero { 0,1, 2, 3....}

• Integers – Positive or negative natural numbers or zero

{ -2, -1, 0, 1, 2,…}

Words to know….Words to know….• Rational Number – any number which can be written as a

fraction.

• Irrational Number – Any decimal number which can’t be written as a fraction.

A non-terminating and non-repeating decimal.

Example –

» Real – rational numbers and irrational numbers.•

....1415926.3

Real NumbersRational Numbers Irrational Numbers

11

2

17

e

4

27 3.0

11

10

4.5

Integers

Whole Numbers

Natural Numbers

-7-1 -3

0

1 23

Sets of Numbers – (using a tree Sets of Numbers – (using a tree map)map)

3 ....1415926.3

Let’s practiceLet’s practiceDirections: Identify each number below as natural, whole, integer,

rational, irrational, or real. More than one answer can apply.

5

4

8

7

0

9Rational, real

Whole, integer, rational, real

integer, rational, real

rational, real

Let’s practiceLet’s practiceDirections: Identify each number below as natural, whole, integer, rational,

irrational, or real. More than one answer can apply.

25

6

8

16irrational, real

Natural, Whole, integer, rational, real

Natural, Whole, integer, rational, real

integer, rational, real

Use <, >, or = to Use <, >, or = to comparecompare

3

26.

8

5 << 65.

9

5 5.

10

33

1

12

121

7

21

6

75

6

25.20

5

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>>

<<

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<<

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Lesson QuizLesson Quiz

2 2

16

Write all classifications that apply to each number.

real, irrationalreal, integer, rational

0

25 94

not a real number rational