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 62232, 52155, 40034 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,

 \[-5,\text{ }-4,\text{ }-3,\text{ }-2,\text{ }-1,\text{ }0,\text{ }+\text{ }1,\text{ }+\text{ }2,\text{ }+\text{ }3\], \[~+\text{ }4,\text{ }+\text{ }5,\text{ }+\text{ }6,\text{ }+\text{ }7\text{ }...........\] 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

 

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

 

Place are 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 568232.

Solution: 500000

 

Face value

Face value of a number is the number itself.

  • Example:

Find the face value of 3 in the number 453282.

Solution: 3

 

Successor

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

 

  • Example:

Find the successor of 4444.     

Solution: \[4444+1=4447\]

 

Predecessor

Predecessor of a number just comes before the number.

  • Example:

Find the predecessor of 4444.

Solution: \[44441=4443\]

 

Roman Numeral

Roman numerals represent the numbers using alphabetical symbols.

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

 

Symbols

I

Value

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 symb01 of smaller value is right to the symbol of greater values are added.

  • Example:

\[LV=50+5=55\]

\[DC=500+100=600\]

 

 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:

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

\[DXC=500+10010=590\]

 

Look at the following table:

 

I

1

 

XXI

21

 

XLI

41

 

LXI

61

 

LXXXI

81

II

2

 

XXII

22

 

XLII

42

 

LXII

62

 

LXXXII

82

III

3

 

XXIII

23

 

XLIII

43

 

LXIII

63

 

LXXXIII

83

IV

4

 

XXIV

24

 

XLIV

44

 

LXIV

64

 

LXXXIV

84

V

5

 

XXV

25

 

XLV

45

 

LXV

65

 

LXXXV

85

VI

6

 

XXVI

26

 

XLVI

46

 

LXVI

66

 

LXXXVI

86

VII

7

 

XXVII

27

 

XLVII

47

 

LXVII

67

 

LXXXVII

87

VIII

8

 

XXVIII

28

 

XLVIII

48

 

LXVIII

68

 

LXXXVIII

88

 IX

9

 

XXIX

29

 

XLIX

49

 

LXIX

69

 

LXXXIX

89

X

10

 

XXX

30

 

L

50

 

LXX

70

 

XC

90

XI

11

 

XXXI

31

 

LI

51

 

LXXI

71

 

XCI

91

XII

12

 

XXXII

32

 

LII

52

 

LXXII

72

 

XCII

92

XIII

13

 

XXXIII

33

 

LIII

53

 

LXXIII

73

 

XCIII

93

XIV

14

 

XXXIV

34

 

LIV

54

 

LXXIV

74

 

XCIV

94

XV

15

 

XXXV

35

 

LV

55

 

LXXV

75

 

XCV

95

XVI

16

 

XXXVI

36

 

LVI

56

 

LXXVI

76

 

XCVI

96

XVII

17

 

XXXVII

37

 

LVII

57

 

LXXVII

77

 

XCVII

97

XVIII

18

 

XXXVIII

38

 

LVIII

58

 

LXXVIII

78

 

XCVIII

98

XIX

19

 

XXXIX

39

 

LIX

59

 

LXXIX

79

 

XCIX

99

XX

20

 

XL

40

 

LX

60

 

LXXX

80

 

C

100

 

 

 

 

 

 

 

 

 

 

 

 

D

500

 

 

 

 

 

 

 

 

 

 

 

 

M

1000

 

 

Note: A symbol can not be repeated more than 3 times.

 

Other Topics

Notes - Number Sense and Numerations
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