Real Number System

Ir ra tion a l N u m be rsp i, sq r t 7

N o n in te g er R a tion a l N um be rs-1 4 /5 , 9 /1 0 , 30 ,13

N eg a tiv e In te ge rs-2 0 , -1 3 , -1

Z e ro0

N a tu ra l N u m b e rs o rP os it iv e In te ge rs

1 , 16 , 1 70

W h o le N u m b e rs0 , 2 , 5 6 , 1 98

In te ge rs-1 0 , 0 , 8

R a tio n a l N u m b e rs-3 5 , -7 /8 , 0 , 5 , 27 /11

R e a l N u m b e r S ys tem-1 8 , -1 /2 , 0 , sq r t 2 , p i , 47 /10

To show how these number are classified, use the Venn diagram. Place the number where it belongs

on the Venn diagram.

9

4

2

1

Rational Numbers

Integers

Whole Numbers

NaturalNumbers

Irrational Numbers

-12.64039…

117

0

6.369

4

-3

The Set of Real NumbersThe Set of Real NumbersThe Set of Real NumbersThe Set of Real Numbers

Q

Q'Q'QQ

ZZWW

NN

The Set of Numbers• Natural Numbers

– The set of natural numbers contains {1, 2, 3,…..}

Whole numbers: The union of zero and Whole numbers: The union of zero and natural number natural number

- { 0 } - { 0 } {1, 2, 3, 4, ….} {1, 2, 3, 4, ….}

- {0, 1, 2, 3, 4, …}- {0, 1, 2, 3, 4, …}

• Integers are the set of whole numbers and their opposites.

{…,-3, -2, a-1, 0, 1, 2, 3,…}

Set of Real Numbers, cont’dRational Numbers –the set of all numbers that can be

expressed as a quotient of integers or

Rational numbers are any numbers that can be expressed in the form of a/b , where a and b are integers, and b ≠ 0.

• They can always be expressed by using terminating decimals or repeating decimals.

• Terminating decimals are decimals that contain a finite number of digits.

• Examples:36.80.1254.5

• Repeating decimals are decimals that contain a infinite number of digits.

• Examples: 0.333… 7.689689…

Irrational Numbers – the set of all numbers that correspond to points on the number line but that are not rational numbers. That is, an irrational number is a number that cannot be expressed as a quotient of integers. or

Irrational numbers are any numbers that cannot be expressed as .

• They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern.

• Examples of irrational numbers:– 0.34334333433334…– 45.86745893…– (pi)– square root of 2 = 3.141592654…_ 0. 01011011101111…

Real Numbers – is the set of all numbers each of which correspond to a point on the number line.

EXAMPLE:Classify all the following numbers as natural, whole, integer,

rational, or irrational. List all that apply.a. 117b. 0c. -12.64039…d. -½e. 6.36f. g. -3

Definition of Sets

- Set of Natural number

N={1, 2, 3, 4, …}

- Set of Integer number

Z={0, ±1, ± 2, ± 3, ± 4, …}

- Set of Rational number

Q={1/2, 1, 3/2, 4, 5/7,…}- Set of Real number

R={1/2, 1, 1.3333,1.41, …}

∩N ∩Z ∩Q R

11.1/2 is an integer

12. 0.5 is an integer

13. Square root of 2 is a rational number

14. Square root of 7 is a real number

15.-3/5 is a rational number

16.0 is a rational number

17. 13/4 is a rational number

18.-5 is both rational and real number.

19.-5/3 is an irrational number

20.21/8 is an irrational number

21.O is a positive number.

22. When zero is added to set of counting numbers set of whole number are formed

23.The natural number, counting number, positive integers are the different name using for the same set of numbers.

24.When the negative integer,positiveinteger,and zero are combined set of integers formed.

25.Any number to the left of zero on the number line is a negative integer.

26.Every negative integers is a real number.

27.Every integer is a rational

28.Every rational number is a real number.

29.Every rational number is a real number.

30.Every negative number is a negative integer

31.Some real numbers are not rational

32.Some rational numbers are not real.

33.The symbol R is used to represent set of real numbers

34.Every integer is positive.

Write true or false and explained with example.

42. A real number but not integer.

43. A rational number but not integer.

44. An integer but not negative integer.

45. A real number but not rational number.

46.An irrational number but not a positive number.

47.An integer and rational number.

48.A negative integer and a real.

49.A negative integer and rational number.

50.A real number but not a rational number.

51. A rational number but not negative number.

52.An integer but not positive integer.

53.A real number but not rational number..

54.What is a rational number?

55.Explaine why every integer is a rational number.