Large Numbers, Systems of Numeration
Lakhs and Crores
We know
that the largest 6-digit number is 9,99,999.
What
happens if you add 1 to it?
9,99,999 + 1 = 10,00,000
We get
the smallest 7-digit number, that is 10,00,000.
It is
read as ten lakh.
What is
the largest 7-digit number? It is 99,99,999.
If you
add 1 to it, you get 1,00,00,000.
99,99,999 +
1 = 1,00,00,000
This is
the smallest 8-digit number. It is read as one crore.
We know about different periods and place values in the number system.
Now, we shall extend this concept beyond six digits. The place to the
left of lakhs is read as ten lakh and one place to the left of ten lakhs
is read as one crore.
Indian System of Numeration
Place Value Chart
The different periods
and places in Indian system are:
The
ones period has 3 places: ones, tens
and hundreds
The
thousands period has 2 places:
thousands and ten thousands
The lakhs period has 2 places: lakhs and
ten lakhs
The crores period has 2 places: crores and
ten crores
|
Crores
|
Lakhs
|
Thousands
|
Ones
|
||||
|
C
|
TL
|
L
|
TTh
|
Th
|
H
|
T
|
O
|
|
5
|
6
|
1
|
7
|
0
|
4
|
6
|
3
|
|
8
|
0
|
4
|
4
|
9
|
0
|
1
|
2
|
The first number is read as:
Five crore sixty-one lakh seventy thousand four hundred
sixty-three
The second
number is read as:
Eight crore four lakh forty-nine thousand twelve
Inserting Commas
The digits in a number can be separated by
putting commas according to the period
they lie in. The digits under the same period are read together and the name of
the period is read alongside. See an example below for the number 28907613.
|
2
|
89
|
07
|
613
|
|
Crores
|
Lakhs
|
Thousands
|
Ones
|
It is read as 2 crore 89
lakh 7 thousand 6 hundred 13.
International System of Numeration
The different periods
and places in international system are:
The
ones period has 3 places: ones, tens and hundreds
The
thousands period has 3 places: thousands, ten thousands and hundred thousands
The millions period has 3 places: millions, ten millions and
hundred millions
The international system has three places for every period. The
place value chart for the international system of numeration is as follows:
|
Millions
|
Thousands
|
Ones
|
||||||
|
HM
|
TM
|
M
|
HTh
|
TTh
|
Th
|
H
|
T
|
O
|
|
|
4
|
3
|
9
|
4
|
7
|
0
|
2
|
5
|
|
6
|
5
|
0
|
1
|
8
|
0
|
3
|
7
|
8
|
In the international system, 43947025
is written as 43,947,025.
It is read as: Forty-three million nine hundred forty-seven
thousand twenty-five
The second number 650180378 is written as 650,180,378.
It is read as: Six hundred fifty million one hundred eighty
thousand three hundred seventy-eight.
Expanded Form
68,25,127 can be written in expanded form as:
60,00,000 + 8,00,000 + 20,000 + 5000 + 100 + 20 + 7.
732,945,436 can be written in expanded form as:
700,000,000 + 30,000,000 + 2,000,000 + 900,000 + 40,000 +
5,000 + 400 + 30 + 6
Read more in detail – Click Here!
Standard Form
To reduce the expanded form 7,00,00,000 + 40,000 + 5000 + 600 + 3
in standard form, arrange the numbers in appropriate columns and then add.
The standard form of the number is 7,00,45,603.
Read more in detail – Click Here!