Indian and International Systems of Numeration

# Indian and International Systems of Numeration

## 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