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.
Find the place value of 5 in the number 568232.
Solution: 500000
Face value
Face value of a number is the number itself.
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.
Find the successor of 4444.
Solution: \[4444+1=4447\]
Predecessor
Predecessor of a number just comes before the number.
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.
\[II=2\times 1=2\]
\[XXX=3\times 10=30\]
Rule 2: The symbols I, X, C, M can be repeated in a roman numeral.
\[CCC=3\times 100=300\]
\[MM=2\times 1000=2000\]
Rule 3: The symbols V, L, and D can not be repeated.
\[DD=2\times 500=1000\]
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.
\[LV=50+5=55\]
\[DC=500+100=600\]
Rule 5: If a symbol of smaller value is left to the symbol of greater value, their difference is the resulting value.
\[VL=505=45\]
\[CD=500100=400\]
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.
\[XIV=10+51=14\]
\[DXC=500+10010=590\]
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.
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