5th Class Mathematics Numbers Number Sense and Numerations

Number Sense and Numerations

Category : 5th Class

 Number Sense and Numerations

 

Numbers

Numbers are mathematical symbol by which we express date, time, distance, position, quantity etc.

We use ten symbols (0, 1, 2. 3, 4, 5, 6, 7, 8, 9) to write any number.

Like 346562232, 34654521155, 4003444656 etc.

 

Number System

Number system deals with the study of different types of numbers. In this chapter, we will study about the categorization of different types of numbers.

 

Natural Numbers

Counting starts with 1 and continue till infinite. Counting numbers are called natural numbers.

For example, 1, 2, 3, 4, 5, 6, 7 ........... etc.

 

Whole Numbers

When 0 is included with natural numbers, they are called whole number. In other words ?Natural numbers together with zero are called whole numbers.?

For example, 0, 1, 2, 3, 4, 5, 6, 7 ............ etc.

 

Integers

Integers are the collection of whole numbers and negative of natural numbers.

For example, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7 ........... Etc.

System of Numeration

Mathematical notation of numbers is called numeration. Let us know about two types of numeration.

(a) Indian system of numeration

(b) International system of numeration

Indian System of Numeration

It is a positional decimal number system. Look at the following place value chart

Period

Kharab

Arab

Crores

Lakhs

Thousands

Ones

 

 

 

 

Places

 

Ten Kharab (T-kh)

1000000000000

Kharab (kh)

100000000000

Ten Arab (T-A)

10000000000

Arab (A)

10000000000

Ten Crores (T-C)

100000000

Crores (C)

10000000

Ten Lakhs (T-L)

1000000

Lakhs (L)

100000

Ten thousands (T-TH)

10000

Thousands (TH)

1000

Hundred (H)

100

Tens (T)

10

Ones (0)

0

                           
  •                Example

Name the number, indicated in the place value chart:

Period

Kharab

Arab

Crores

Lakhs

Thousands

Ones

 

 

 

Places

Ten Kharab (T-kh)

1000000000000

Kharab (kh)

100000000000

Ten Arab (T-A)

10000000000

Arab (A)

1000000000

Ten Crores (T-C)

100000000

Crores (C)

10000000

Ten Lakhs (T-L)

1000000

Lakhs (L)

100000

Ten thousands (T-TH)

10000

Thousands (TH)

1000

Hundred (H)

100

Tens (T)

10

Ones (0)

0

 

1

4

0

2

6

5

2

1

0

3

2

5

3

 Solution:

            Fourteen kharab two arab sixty five crore twenty one lakh three thousand two hundred fifty three.

 

International System of Numeration

This system is applied in whole world. The following place value chart shows the international system of numeration.

Period

Trillions

Billion

Million

Thousands

Ones

 

 

 

 

 

Places

Hundred Trillion

(100000000000000)

Ten Trillions

(10000000000000)

Trillions

(1000000000000)

Hundred billions

(100000000000)

Ten billions

(10000000000)

Billions

(1000000000)

Hundred millions

(100000000)

Ten millions

(10000000)

Millions

(1000000)

Hundred thousands

(100000)

Ten thousands

(10000)

Thousands

(1000)

Hundred

(100)

Tens

(10)

Ones

(0)

                               
  •           Example:

Name the number indicated in the place value chart.

Period

Trillion

Billions

Million

Thousands

Ones

Places

Hundred Trillions

(100000000000000)

Ten Trillions

(10000000000000)

Trillions

(1000000000000)

Hundred billions

(100000000000)

Ten billions

(10000000000)

Billions

(1000000000)

Hundred millions

(100000000)

Ten million

(10000000)

Millions

(10000000)

Hundred thousands

(100000)

Ten thousands

(10000)

Thousands

(1000)

Hundred

(100)

Tens

(10)

Ones

(0)

 

5

4

6

5

6

8

0

2

2

0

6

5

2

1

5

 

Solution:

Five hundred forty six trillion five hundred sixty eight billion twenty two million sixty five thousands two hundred fifteen.

 

Place Value

Place value of a digit in a number is the position it occupies according to the place value chart.

  •           Example:

Find the place value of 5 in the number 646568232.

Solution: 500000

Face Value

Face value of a number is the number itself.

  •           Example:

Find the face value of 3 in the number 451453282.

Solution: 3

Successor

The number which comes just after a number is called successor of that number.

 

  •             Example:

Find the successor of 5456446.

            Solution: 54564446 + 1 = 54564447

Predecessor

Predecessor of a number just comes before the number.

  •           Example:

Find the predecessor of 4665655416.

            Solution: 4665655416 ? 1 = 4665655415

Roman Numeral

Roman numerals the number using alphabetical symbols.

The seven alphabetical symbols, which are used in Roman system of numeration, and their values are as follows:

Symbols

Value

I

1

V

5

X

10

L

50

C

100

D

500

M

1000

Rules for Using Symbols

Rule1: When a symbol is repeated, its value is multiplied as many times as the symbol is repeated.

  •           Example:

\[II=2\times 1=2\]

\[XXX=3\times 10=30\]

Rule 2: The symbols I, X, C, M can be repeated in a roman numeral.

  •            Example:

\[CCC=3\times 100=300\]

\[MM=2\times 1000=2000\]

Rule 3: The symbols V, L, and D can not be repeated.

  •            Example:

\[DD=2\times 500=1000\]

But 1000 is represented by symbol M.

Therefore, the above expression is not correct.

Rule 4: If a symbol of smaller value is right to the symbol to greater value, their values are added.

  •            Example:

\[LV=50\times 5=55\]

\[DC=500\times 100=600\]

Rule 5: If a symbol of smaller value is left to the symbol of greater value, their difference is the resulting value.

  •         Example

\[VL=50-5=45\]

\[CD=500-100=400\]

Rule 6: If a symbol of smaller value comes between two symbols of larger value, its value is subtracted from the value of the symbol, which is right to it.

  •        Example

\[XIV=10+5-1=14\]

\[DXC=500+100-10=590\]

Look at the following table:

 I

1

 

XXVI

26

 

LI

51

 

LXXVI

76

II

2

 

XXVII

27

 

LII

52

 

LXXVII

77

III

3

 

XXVIII

28

 

LIII

53

 

LXXVIII

78

IV

4

 

XXIX

29

 

LIV

54

 

LXXIX

79

V

5

 

XXX

30

 

LV

55

 

LXXX

80

VI

6

 

XXXI

31

 

LVI

56

 

LXXXI

81

VII

7

 

XXXII

32

 

LVII

57

 

LXXXII

82

VIII

8

 

XXXIII

33

 

LVIII

58

 

LXXXIII

83

IX

9

 

XXXIV

34

 

LIX

59

 

LXXXIV

84

X

10

 

XXXV

35

 

LX

60

 

LXXXV

85

XI

11

 

XXXVI

36

 

LXI

61

 

LXXXVI

86

XII

12

 

XXXVII

37

 

LXII

62

 

LXXXVII

87

XIII

13

 

XXXVIII

38

 

LXIII

63

 

LXXXVIII

88

XIV

14

 

XXXIX

39

 

LXIV

64

 

LXXXIX

89

XV

15

 

XL

40

 

LXV

65

 

XC

90

XVI

16

 

XLI

41

 

LXVI

66

 

XCI

91

XVII

17

 

XLII

42

 

LXVII

67

 

XCII

92

XVIII

18

 

XLIII

43

 

LXVIII

68

 

XCIII

93

XIX

19

 

XLIV

44

 

LXIX

69

 

XCIV

94

XX

20

 

XLV

45

 

LXX

70

 

XCV

95

XXI

21

 

XLVI

46

 

LXXI

71

 

XCVI

96

XXII

22

 

XLVII

47

 

LXXII

72

 

XCVII

97

XXIII

23

 

XLVIII

48

 

LXXIII

73

 

XCVIII

98

XXIV

24

 

XLIX

49

 

LXXIV

74

 

XCIX

99

XXV

25

 

L

50

 

LXXV

75

 

C

100

 

 

 

 

 

 

 

 

 

D

500

 

 

 

 

 

 

 

 

 

M

1000

 

Note: A symbol cannot be repeated more than 3 times.



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