Number
System
Knowing Numbers:
Natural Numbers: Counting numbers are called as natural numbers.
Denote as N= { 1,2,3,4,5,6,7,8,9 }
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
Whole
Numbers: If zero is included in the set of natural
numbers known as whole numbers.
Denote as W= { 0,1,2,3,4,5,6,7,8,9 }
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
The numbers
are written with the help of symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 knows as
digits.
Expressing a number: Right to left
10x10x10x10
|
10x10x10
|
10x10
|
10
|
1
|
Ten
Thousand
|
Thousand
|
Hundred
|
Ten
|
Ones
|
Example: 67138
Sixty Seven Thousand One Hundred Thirty Eight
6
|
7
|
1
|
3
|
8
|
Ten
Thousand
|
Thousand
|
Hundred
|
Ten
|
Ones
|
= 6 x 10000
+ 7 x 1000 + 1 x 100 + 3 x 10 + 8 x 1
= 60000 +
7000 + 100 + 30 + 8
= 67138
Comparing and Ordering:
Comparison
of numbers starts from first digit of numbers from the left to right hand side.
Example 1: Compare 8534 and 8713
Number 1
|
Number 2
|
Compare
|
|
8
|
8
|
8 = 8
|
Compare next digit
|
5
|
7
|
5 < 7
|
Stop Comparing
|
Number 8713
> Number 8534
Example 2: Compare 4635 and 4619
Number
1
|
Number
2
|
Compare
|
Steps
|
4
|
4
|
4 = 4
|
Compare next digit
|
6
|
6
|
6 = 7
|
Compare next digit
|
3
|
1
|
3 > 1
|
Stop Comparing
|
Number 4635
> Number 4619
Successor and Predecessor:
Successor
of number is finding by adding 1 to the number.
Successor
= Number + 1
|
Predecessor
of number is finding by subtracting by 1 to the number.
Predecessor
= Number - 1
|
Successor =
Number + 1
Periods – The Indian System of Numeration:
Periods
|
Crores
|
Lakhs
|
Thousands
|
Ones
|
|||||
Places
|
Ten
Crores
|
Crores
|
Ten
Lakhs
|
Lakhs
|
Ten
Thousands
|
Thousands
|
Hundreds
|
Tens
|
Ones
|
TC
|
C
|
TL
|
L
|
T-Th
|
Th
|
H
|
T
|
O
|
|
100000000
|
10000000
|
1000000
|
100000
|
10000
|
1000
|
100
|
10
|
1
|
|
Example: A number write as 64,32,96,563
|
|||||||||
*A
comma is put after first three digits then after every two digits start from
right.
Example: A number 643296563 is write
as 64,32,96,563
Periods – The International System of Numeration:
Periods
|
Billions
|
Millions
|
Thousands
|
Ones
|
||||||||
Places
|
Hundred
Billions
|
Ten
Billions
|
Billions
|
Hundred
Millions
|
Ten
Millions
|
Millions
|
Hundred
Thousands
|
Ten Thousands
|
Thousands
|
Hundreds
|
Tens
|
Ones
|
HB
|
TB
|
B
|
HM
|
TM
|
M
|
H-Th
|
T-Th
|
Th
|
H
|
T
|
O
|
|
100000000000
|
10000000000
|
1000000000
|
100000000
|
10000000
|
1000000
|
100000
|
10000
|
1000
|
100
|
10
|
1
|
|
1011
|
1010
|
109
|
108
|
107
|
106
|
105
|
104
|
103
|
102
|
101
|
100
|
|
*A
comma is put after every three digits from the right.
Example: A number 74543231782 is write
as 74,543,231,782
Note: One
Trillion is 1000 billion.
Use of Numbers in daily life:
Numbers are
used to measuring the length, distances, weights and amounts.
Small
lengths are measured in millimeter (mm) and centimeter whereas larger lengths
are measured in meter (m) and kilometer (km).
1 Meter (M) = 100 cm
(centimeter) = 10000 mm (millimeter)
|
1 Kilometer = 1000 M
x 1000 = 1000000 mm
|
1 Gram = 1000 mg and
1 kg (Kilogram) = 1000 gm (gram)
|
1 Kilogram = 1000 gm
x 1000 = 1000000 mg (milligram)
|
1 Liter (L) = 1000
ml and 1 kL (Kiloliter) = 1000 L
|
1 Kiloleter = 1000 L
x 1000 = 1000000 ml (milliliter)
|
Roman Numerals:
The Romans
symbols are:
Roman Symbols
|
I
|
V
|
X
|
L
|
C
|
D
|
M
|
Meanings
|
1
|
5
|
10
|
50
|
100
|
500
|
1000
|
Example: Can be calculated as:
III = 1 + 1 +1 = 3
|
XXX = 10 + 10 + 10 =
30
|
CC = 100 + 100 = 200
|
CCC = 100 + 100 +
100 = 300
|
MM = 1000 + 1000 =
2000
|
Exercise:
Question 1: Write the natural numbers?
Question 2: Write the whole numbers?
Question 3: Zero is neither positive nor negative (True /
False)?
Question 4: Write the number 35409 in numerals?
Question 5: Compare the number 67518 and 67499?
Question 6: Write the number 3558409 in numerals?
Question 7: Fill in
the blanks
(a) 1
Meter = _____ Centimeter
(b) 1
KM = _______Meter
(c) 1
KG = _______ gm
(d)1
KL = _______ ml
Question 8: Fill in the blanks
(a) VI = ______
(b) XI
= _______
(c) XXXVII
= _______
(d)CD
= _______
