Long before the numbers were invented, the counting was done using some kind of physical objects such as sticks or pebbles. Post that, lines and marks on rocks and potteries also continued for a long time for counting various things. Eventually, the numbers came into existence. And then there was a need to adopt a standard system for counting, that is, a mathematical notation for expressing numbers using digits or symbols. This is known as the numeral system or the system of numeration. But across different countries and periods, the numbers developed also differed. This is one reason we have a large number of numeral systems, e.g., Roman, Greek, Arabic, binary, decimal, etc. However, here we would confine our discussion to Indian and international numeral system.

## Indian Numeral System

Let us consider a number, say 225. Notice that the digit 2 is used twice in this number. Both of them have a different value. We differentiate them by stating their **place value,** which is defined as the numerical value of a digit on the basis of its position in a number. So the place value of the leftmost 2 is Hundreds while the one in the center is Tens.

Coming back to the Indian numeral system, the place values of digits go in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores and so on.

In the number *10,23,45,678* the place values of each digit are:

- 8 – Ones
- 7 – Tens
- 6 – Hundreds
- 5 – Thousands
- 4 – Ten Thousands
- 3 – Lakhs
- 2 – Ten Lakhs
- 0 – Crores
- 1 – Ten Crores

The relationship between them is:

- 1 hundred = 10 tens
- 1 thousand = 10 hundreds = 100 tens
- 1 lakh = 100 thousands = 1000 hundreds
- 1 crore = 100 lakhs = 10,000 thousands

### International Numeral System

The place values of digits go in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions and so on, in the international numeral system. In the number *12,345,678* the place values of each digit are:

- 8 – Ones
- 7 – Tens
- 6 – Hundreds
- 5 – Thousands
- 4 – Ten Thousands
- 3 – Hundred Thousands
- 2 – Millions
- 1 – Ten Millions

The relations between them are:

- 1 hundred = 10 tens
- 1 thousand = 10 hundreds = 100 tens
- 1 million = 1000 thousands
- 1 billion = 1000 millions

Comparison between Indian and International Numeral System

Comparing the two numeral systems we observe that:

- 100 thousands = 1 lakh
- 1 million = 10 lakhs
- 10 millions = 1 crore
- 100 millions= 10 crores

### Placement of Comma

Commas are placed in the large numbers to help us read and write them easily. In Indian and international systems, the commas are placed at different positions.

As per Indian numeral system, the first comma is placed after the hundreds place post which they are placed after every two digits. E.g., 1,23,45,67,890

As per international numeral system, the first comma is placed after the hundreds place, post which they are placed after every three digits. E.g., 1,234,567,890

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