Indian Numeral System

What is the Indian Numeral System?

The Indian numeral system contains numerals that are used to represent the numbers using a set of symbols. This system can be distinguished from the other numeral systems based on the nomenclature followed for different place values. When we use the Indian numeral system, we count with ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, and crores.

The following table depicts the different periods and places according to the number of digits in a number.

Use of Separators​

According to the Indian numeral system, separators (comma) are used after every period while representing a number in its standard numeral form. For example, the number 384756182 can be better represented as 38,47,56,182 in the standard Indian numeral system form using separators after every period.

The number names in the Indian numeral system depend upon the nomenclature for different place values of digits in the number. While writing number names of the numerals in the Indian system, we should consider the following points:

• According to the Indian numeral system, separators are marked to distinguish different periods.
• Therefore, while writing the number names, these periods can be used to read the different place values in the number. 
• Using these place values, we can write the number names accordingly.

For example, the number name for 38,47,56,182 is written as thirty-eight crore, forty-seven lakh fifty-six thousand, one hundred and eighty-two.

The following figure shows how to write the number name for 38,47,56,182, with the help of the Indian place value chart. We read the number according to the place values of all the digits given here. 

​​So, we concluded that it is easy to read any large number if we place the number in the Indian place value chart of the Indian numeral system.

The main difference between the Indian and International numeration systems is the placement of the separators (commas) and the nomenclature of different place values. The International numeral system is used worldwide. When we count in terms of ones, hundreds, thousands, ten thousand, hundred thousand, millions, and billions, we are referring to the International numeral system. The following table depicts different places and periods according to the number of digits in a number. 

The following table highlights the differences between the Indian and the International numeral system.

For example: Rewrite the number 1347823 in the International numeral system and the Indian numeral system, using commas. How will you read this number according to both the systems?

Solution:

In the International numeral system, we begin from the right side and insert commas after every three digits. We divide the number into periods and read the period separately.

Standard International numeral form: 1,347,823
Number Name: One million, three hundred forty-seven thousand, eight hundred twenty-three.

The same given number, 1347823, can be written in the Indian numeral system, in the following way:

Standard Indian numeral form: 13,47,823 
Number Name: Thirteen lakh, Forty-seven thousand, eight hundred and twenty-three.

What are the Indian Numerals?

Indian numerals consist of 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These symbols came into existence during the 6^th or 7^th century in India and are used in the Indian numeral system (or system of numeration) for expressing numbers.

What is the Indian Number System in Maths?

The Indian numeral system (or system of numeration) is a writing system adapted in India for expressing numbers. It is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. In the Indian number system, the place values of digits are read in the order of Ones, Tens, Hundreds, and so on, based on the nomenclature of the different periods.

What are Number Names in the Indian Numeral System?

When numbers are expressed in the form of words, the representation is termed as its number name. In the Indian numeral system, the number names depend on the different place values of digits in the number.

For example, the number name for 38,47,56,182 is written as Thirty-eight crore, forty-seven lakh, fifty-six thousand, one hundred and eighty-two.

What are the Differences Between the Indian Numeral System and the International Numeral System?

The differences between the Indian and the International numeral system are given as follows:

• In the Indian numeral system, nine places are grouped into four periods: ones, thousands, lakhs, and crores. While, in the International number system nine places are grouped into three periods: ones, thousands, and millions, followed by period billions and so on.
• In the Indian numeral system, place values are marked as ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores. While, in the International numeral system, place values are marked as ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million, and so on. 
• The use of separators is different for both the Indian and International numeral systems, depending upon the periods.

How are Numerals Written in the Indian System?

The numbers in the Indian numeral system are separated by commas (separators) after every period, as defined by this system. Starting from the right end, the first comma is placed just before the digit at the hundreds place, the next comma is placed just before the digit at ten thousand's place, followed by the digit after ten lakhs, and so on. For example, the number 781700182 is written as 78,17,00,182.

How do you Write Number Names in the Indian Numeral system?

While writing number names, we should know the place value of each digit according to the Indian place value system. The separators (commas) help us to read the place values of the numbers as we start writing them from left to right. So, start writing the name of the period after each number in the period. Skip the period which has zeros at all places.

For example, the number name for 41,27,56,082 is written as forty-one crore, twenty-seven lakh, fifty-six thousand, and eighty-two.

What Comes after 10 crores in the Indian System?

The place value that comes after 10 crores is 100 crores or 1 Arab.