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REAL NUMBERS (as opposed to fake numbers?) REAL NUMBERS (as opposed to fake numbers?)

REAL NUMBERS (as opposed to fake numbers?) - PowerPoint Presentation

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REAL NUMBERS (as opposed to fake numbers?) - PPT Presentation

Objective TSW identify the parts of the Real Number System TSW define rational and irrational numbers TSW classify numbers as rational or irrational Real Numbers Real Numbers are every number Therefore any number that you can find on the number line ID: 696047

number numbers irrational rational numbers number rational irrational real integers written line decimals fraction order natural examples repeating additional

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Slide1

REAL NUMBERS

(as opposed to fake numbers?)Slide2

Objective

TSW identify the parts of the Real Number SystemTSW define rational and irrational numbersTSW classify numbers as rational or irrationalSlide3

Real Numbers

Real Numbers are every number.Therefore, any number that you can find on the number line.

Real Numbers have two categories.Slide4

What does it Mean?

The number line goes on forever.Every point on the line is a REAL number.

There are no gaps on the number line.

Between the whole numbers and the fractions there are numbers that are decimals but they don’t terminate and are not recurring decimals. They go on forever.Slide5

Real Numbers

REAL NUMBERS

-8

 

-5,632.1010101256849765…

 

61

49%

π

 

549.23789

154,769,852,354

1.333Slide6

Two Kinds of Real Numbers

Rational Numbers

Irrational NumbersSlide7

Rational Numbers

A rational number is a real number that can be written as a fraction.

A rational number written in decimal form is terminating or repeating.Slide8

Examples of Rational Numbers

161/2

3.56

-8

1.3333…

- 3/4Slide9

Integers

One of the subsets of rational numbersSlide10

What are integers?

Integers are the whole numbers and their opposites.Examples of integers are

6

-12

0

186

-934Slide11

Integers are rational numbers because they can be written as fraction with 1 as the denominator.Slide12

Types of Integers

Natural Numbers(N):

Natural Numbers are counting numbers from 1,2,3,4,5,................

N

= {1,2,3,4,5,................}

Whole Numbers (W):

Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............

W

= {0,1,2,3,4,5,..............}

W = 0 + NSlide13

WHOLE

Numbers

REAL NUMBERS

IRRATIONAL

Numbers

NATURAL

Numbers

RATIONAL

Numbers

INTEGERSSlide14

Irrational Numbers

An irrational number is a number that cannot

be written as a fraction of two integers.

Irrational numbers written as decimals are non-terminating and non-repeating.Slide15

A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.

Caution!

Irrational numbers

can be written only as decimals that do

not

terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. Slide16

Examples of Irrational Numbers

 

Pi

 Slide17

Try this!

a) Irrational

b) Irrational

c) Rational

d) Rational

e) IrrationalSlide18

Additional Example 1: C

lassifying Real Numbers

Write all classifications that apply to each number.

5 is a whole number that is not a perfect square.

5

irrational, real

–12.75 is a terminating decimal.

–12.75

rational, real

16 2

whole, integer, rational, real

= = 2

4 2

16 2

A.

B.

C.Slide19

A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.Slide20

State if each number is rational, irrational, or not a real number.

21

irrational

0 3

rational

0 3

= 0

Additional Example 2: D

etermining the Classification of All Numbers

A.

B.Slide21

not a real number

Additional Example 2: D

etermining the Classification of All Numbers

4

0

C.

State if each number is rational, irrational, or not a real number.Slide22

Objective

TSW compare rational and irrational numbersTSW order rational and irrational numbers on a number lineSlide23

Comparing Rational and Irrational Numbers

When comparing different forms of rational and irrational numbers, convert the numbers to the same form.

Compare -3 and -3.571

(convert -3 to -3.428571…

-3.428571… > -3.571

3

7

3

7Slide24

Practice

 Slide25

Ordering Rational and Irrational Numbers

To order rational and irrational numbers, convert all of the numbers to the same form.You can also find the approximate locations of rational and irrational numbers on a number line.Slide26

Example

Order these numbers from least to greatest.

¹/

, 75%, .04, 10%,

⁹/₇

¹/₄ becomes 0.25

75% becomes 0.75

0.04 stays 0.04

10% becomes 0.10

⁹/₇ becomes 1.2857142…

Answer:

0.04, 10%,

¹/

₄, 75%, ⁹/₇ Slide27

Practice

Order these from least to greatest: