System of Numeration – Indian & International

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Numbers play an important role in our lives. Almost all the things we do involve numbers and Mathematics. Our life revolved around numbers since the day we were born. There are countless numbers directly or indirectly connected to our lives. The way of representing numbers consistently using digits or other symbols is called a system of numeration.

Let’s understand what is meant by a system of numeration and what are different types of systems of numeration.

What is Meant by the System of Numeration?

The system of numeration includes numerals, which are symbols that are used to represent numbers. Based on the nomenclature used for distinct place values, a system is identified from other numeral systems. The two most important features of any numeral system are the periods(commas) and number names. Different numeral systems use periods to group the digits differently and have different number names.

  • Periods: Periods (commas) are used after every period in the systems of numeration when representing a number(generally large numbers) in its standard numeral form. For example, the number $890237314$ is written as $89,02,37,314$ or $890,237,314$.
  • Number Names: The nomenclature for different place values of digits in the number determines the number names in any numeral system. For example, Lakh, and Crore are the number names used in the Indian system of numeration, whereas Million, and Billion are used in the International system of numeration.  

There are many types of systems of numeration, but the two most widely used systems of numeration are 

  • Indian System of Numeration
  • International System of Numeration

What is Indian System of Numeration?

The Indian numeral system is a writing system adapted in India for expressing numbers. It is a mathematical notation for representing numbers of a given set, consistently using digits or other symbols. This numeral system comprises a set of numerals formed by $10$ symbols – $0, 1, 2, 3, 4, 5, 6, 7, 8,$ and $9$.

The nomenclature used for numbers in the Indian system of numeration are ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, and crores.

Indian Place Value Chart

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

PeriodNumber NameDigits
CroresTen Crores $(\text{T C})$ $10,00,00,000$$9$
Crores $(\text{C})$ $1,00,00,000$$8$
LakhsTen Lakhs $(\text{T L})$ $10,00,000$$7$
Lakhs $(\text{L})$ $1,00,000$$6$
ThousandsTen Thousands $(\text{T Th})$ $10,000$$5$
Thousands $(\text{Th})$ $1,000$$4$
OnesHundreds $(\text{H})$ $100$$3$
Tens $(\text{T})$ $10$$2$
Ones $(\text{O})$ $1$$1$

Examples of Numbers in Indian System of Numeration 

Example 1: Write $89342845$ in words using the Indian system of numeration.

The number of digits in $89342845$ is $8$ and it can be written in words as Eight Crore Ninety Three Lakh Forty Two Thousand Eight Hundred Forty Five.

Example 2: Write $394794182$ in words using the Indian system of numeration.

The number of digits in $394794182$ is $9$ and it can be written in words as Thirty Nine Crore Forty Seven Lakh Ninety Four Thousand One Hundred Eighty Two.

Example 3: Write $7123486$ in words using the Indian system of numeration.

The number of digits in $7123486$ is $7$ and it can be written in words as Seventy One Lakh Twenty Three Thousand Four Hundred Eighty Six.

Example 4: Write $69283$ in words using the Indian system of numeration.

The number of digits in $69283$ is $5$ and it can be written in words as Sixty Nine Thousand Two Hundred Eighty Three.

Example 5: Write $721894$ in words using the Indian system of numeration.

The number of digits in $721894$ is $6$ and it can be written in words as Seven Lakh Twenty One Thousand Eight Hundred Ninety Four.

Example 6: Write $8932$ in words using the Indian system of numeration.

The number of digits in $8932$ is $4$ and it can be written in words as Eight Thousand Nine Hundred Thirty Two.

Periods​ in Indian System of Numeration

According to the Indian system of numeration, periods(commas) are used after every period while representing a number in its standard numeral form. In this system, the periods are divided according to the rule of $3:2:2$. This means that starting from the right, the first comma is placed after $3$ digits, then the next commas are placed after every $2$ digits.

Examples on Periods​ in Indian System of Numeration

Example 1: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for $94582173$.

According to the Indian system of numeration, $94582173$ can be written as $9,45,82,173$ and is read as Nine Crore Forty Five Lakh Eighty Two Thousand One Hundred Seventy Three.

Example 2: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for $823793742$.

According to the Indian system of numeration, $823793742$ can be written as $82,37,93,742$ and is read as Eighty Two Crore Thirty-Seven Lakh Ninety Three Thousand Seven Hundred Forty Two.

Example 3: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for $6239216$.

According to the Indian system of numeration, $6239216$ can be written as $62,39,216$ and is read as Sixty Two Lakh Thirty Nine Thousand Two Hundred Sixteen.

Example 4: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for $78564$.

According to the Indian system of numeration, $78564$ can be written as $78,564$ and is read as Seventy Eight Thousand Five Hundred Sixty Four.

Example 5: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for $128475$.

According to the Indian system of numeration, $128475$ can be written as $1,28,475$ and is read as One Lakh Twenty Eight Thousand Four Hundred Seventy Five.

What is International System of Numeration?

The Internation numeral system is a writing system followed by most countries worldwide for expressing numbers. It is a mathematical notation for representing numbers of a given set, consistently using digits or other symbols. This numeral system comprises a set of numerals formed by $10$ symbols – $0, 1, 2, 3, 4, 5, 6, 7, 8,$ and $9$.

The nomenclature used for numbers in the International system of numeration are ones, tens, hundreds, thousands, ten thousand, hundred thousand, million, ten million, hundred million, and billion. 

International Place Value Chart

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

PeriodNumber NameDigits
BillionsBillions $(\text{B})$ $1,000,000,000$$10$
MillionsHundred Millions $(\text{H M})$ $100,000,000$$9$
Ten Millions $(\text{T M})$ $10,000,000$$8$
Millions $(\text{M})$ $1,000,000$$7$
ThousandsHundred Thousands $(\text{H Th})$ $100,000$$6$
Ten Thousands $(\text{T Th})$ $10,000$$5$
Thousands $(\text{Th})$ $1,000$$4$
OnesHundreds $(\text{H})$ $100$$3$
Tens $(\text{T})$ $10$$2$
Ones $(\text{O})$ $1$$1$

Examples of Numbers in International System of Numeration 

Example 1: Write $78652987$ in words using the International system of numeration.

The number of digits in $78652987$ is $9$ and it can be written in words as Seventy Eight Million Six Hundred Fifty Two Thousand Nine Hundred Eighty Seven.

Example 2: Write $1842952856$ in words using the International system of numeration.

The number of digits in $1842952856$ is $10$ and it can be written in words as One Billion Eight Hundred Forty Two Million Nine Hundred Fifty Two Thousand Eight Hundred Fifty Six.

Example 3: Write $3723895$ in words using the International system of numeration.

The number of digits in $3723895$ is $7$ and it can be written in words as Three Million Seven Hundred Twenty Three Eight Hundred Ninety Five.

Example 4: Write $658934$ in words using the International system of numeration.

The number of digits in $658934$ is $6$ and it can be written in words as Six Hundred Fifty Eight Thousand Nine Hundred Thirty Four.

Periods​ in International System of Numeration

According to the International system of numeration, periods(commas) are used after every period while representing a number in its standard numeral form. In this system, the periods are divided according to the rule of $3:3:3$. This means that starting from the right, the first comma is placed after every $3$ digit.

Examples on Periods​ in International System of Numeration

Example 1: Using the rules of the International number system, place the commas correctly in the given number and write the number name for $9566218325$.

According to the International system of numeration, $9566218325$ can be written as $9,566,218,325$ and is read as Nine Billion Five Hundred Sixty Six Million Two Hundred Eighteen Thousand Three Hundred Twenty Five.

Example 2: Using the rules of the International number system, place the commas correctly in the given number and write the number name for $845787431$.

According to the International system of numeration, $845787431$ can be written as $845,787,431$ and is read as Eight Hundred Forty Five Million Seven Hundred Eighty Seven Thousand Four Hundred Thirty One.

Example 3: Using the rules of the International number system, place the commas correctly in the given number and write the number name for $56329831284$.

According to the International system of numeration, $56329831284$ can be written as $56,329,831,284$ and is read as Fifty Six Billion Three Hundred Twenty Nine Million Eight Hundred Thirty One Thousand Two Hundred Eighty Four.

Converting Numbers Between Indian and International Systems of Numeration

 To convert a number from the Indian system to the International system first of all remove the periods (commas) from the number and again insert the periods (commas) using the $3:3:3$ format.  To convert a number from the International system to the Indian system first of all remove the periods (commas) from the number and again insert the periods (commas) using the $3:2:2$ format.  

Examples on Converting Numbers Between Indian and International Systems of Numeration

Example 1: Rewrite Three Lakh Fifty Eight Thousand Four Hundred Sixty Nine using the International system of numeration.

Three Lakh Fifty Eight Thousand Four Hundred Sixty Nine is $3,58,469$.

After removing periods the number becomes $358469$.

Inserting periods according to the International system of numeration, we get $358,469$ which is Three Hundred Fifty Eight Thousand Four Hundred Sixty Nine.

Example 2: Rewrite Forty Nine Crore Sixty Four Lakh Thirty Eight Thousand One Hundred Twenty Seven using the International system of numeration.

Forty Nine Crore Sixty Four Lakh Thirty Eight Thousand One Hundred Twenty Seven is $49,64,38,127$.

After removing periods the number becomes $496438127$.

Inserting periods according to the International system of numeration, we get $496,438,127$ which is Four Hundred Ninety Six Million Four Hundred Thirty Eight Thousand One Hundred Twenty Seven.

Example 3: Rewrite Forty Eight Million One Hundred Fifty Six Thousand Seven Hundred Seventeen using the Indian system of numeration.

Forty Eight Million One Hundred Fifty Six Thousand Seven Hundred Seventeen is $48,156,717$.

After removing periods the number becomes $48156717$.

Inserting periods according to the Indian system of numeration, we get $4,81,56,717$ which is Four Crore Eighty One Lakh Fifty Six Thousand Seven Hundred Seventeen.

Difference Between Indian and International Systems of Numeration

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

Indian System of NumerationInternational System of Numeration
Nine places are grouped into four periods: ones, thousands, lakhs, and crores.Nine places are grouped into three periods: ones, thousands, and millions.
Place Values: ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores.Place Values: Ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million.
Lakhs and crores are used in large numbers in the Indian Numeral System.Millions and billions are used in large numbers in the International Numeral System.

Practice Problems

  1. Write the following numbers in words according to the International system of numeration.
    • $67740$
    • $9023421$
    • $70008256$
    • $2893459$
    • $90345216$
  2. Write the following numbers in words according to the Indian system of numeration.
    • $67740$
    • $9023421$
    • $70008256$
    • $2893459$
    • $90345216$
  3. Rewrite the following numbers using the International system of numeration.
    • Thirteen Crore Fifteen Lakh Twenty Eight Thousand Two Hundred Fifty Six
    • Five Crore Four Lakh Ninety Nine Thousand Seven
  4. Rewrite the following numbers using the Indian system of numeration.
    • One Million Four Thirty Six Thousand Three Hundred Ninety Five
    • Twenty Nine Million Six Hundred Nine Thousand Seven Hundred Sixty Two

FAQs

What is the Indian System of Numeration?

The Indian 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 in a consistent manner. In this system, the place values of digits are read in the order of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, Ten Crores, and so on.

What is the International System of Numeration?

The International system of numeration is a writing system used in most countries of the world. for expressing numbers. It is a mathematical notation for representing numbers of a given set, using digits in a consistent manner. In this system, the place values of digits are read in the order of Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousand, Million, Ten Million, Hundred Million, Billion, and so on.

What is the difference between the Indian and the International system of numeration?

The differences between the Indian and the International system of numeration are given as follows.
a) In the Indian system of numeration, nine places are grouped into three periods: ones, thousands, lakhs, and crores. While, in the International system of numeration nine places are grouped into the following periods: ones, thousands, and millions.

b) In the Indian system of numeration, the place values are marked as ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores. While, in the International system of numeration, place values are marked as ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million, and so on.

How are numbers written in the Indian system of numeration?

The numbers in the Indian system of numeration are separated by periods (commas) after every period, as defined by this system. Starting from the right end, the first comma is placed after $3$ digits, then the next commas are placed after every $2$ digit. For example, the number $893428324$ is written as $89,34,28,324$.

What comes after $10$ crores in the Indian system of numeration?

The place value that comes after $10$ crores is $1$ Arab ($1,00,00,00,000$).

How many zeros in $1$ Billion in the International number system?

In the international number system, $1$ billion = $1,000,000,000$. Therefore, there are $9$ zeros in $1$ billion.

Conclusion

The system of numeration uses symbols or digits to represent numbers. The two most widely used systems of numeration are the Indian system of numeration and the International system of numeration. Lakhs and crores are used in large numbers in the Indian Numeral System while Millions and billions are used in large numbers in the International Numeral System.

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