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Numeral systems or systems of numerations are the standard writing systems of counting used to express the numbers using symbols or digits consistently. The most commonly preferred numeral system is the Hindu - Arabic System with a positional base of 10. It contains a set of 10 symbols; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, to comprise a standard number. The two types of the numeral systems discussed are Indian numeral system and International numeral system. Commas, also known as separators, are used to separate the different periods in a number, hence making the place values easily distinguishable while naming. The difference of international numerical system from the Indian numeral system lies in the nomenclature and place value of the digits and grouping of periods.
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Key Terms: Numeral System, Place values, Nomenclature, Indian Numeral System, International Numeral System, Face values
Indian Numeral System
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Indian Numeral System is the standard writing system prevalent in India for the expression of numbers and counting. The uniqueness of the system is based on the nomenclature of the numbers. The naming of numbers in the system depends on the place value of the digits present in it. The place values are arranged in the sequence from left to right as Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, Ten Crores.
The Indian Numeral System follows the nine places - four periods system and the main four periods are Ones, Thousands, Lakhs, and Crores respectively. The main units of the Indian Numeral System are Lakhs and Crores. The separators are used to read place values of the Indian number by distinguishing and separating the four periods using commas. The first comma (or separator) in a number of Indian numeral systems is placed after the Hundreds place value post which the separators are marked after every two digits prevailing. For example, 12,34,45,789 is a number in the Indian numeral system.
| Periods | Place values | Number of symbols or digits |
|---|---|---|
| Crores | Ten Crores | 9 |
| Crores | 8 | |
| Lakhs | Ten Lakhs | 7 |
| Lakhs | 6 | |
| Thousands | Ten Thousands | 5 |
| Lakhs | 4 | |
| Ones | Hundreds | 3 |
| Tens | 2 | |
| Ones | 1 |
International Numeral System
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International Numeral System is the internationally acknowledged standard writing system for the expression of numbers and counting. The place values of the system are arranged in the sequence from left to right as Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Ten Million, and Hundred Millions.
International Numeral System follows the nine places - three periods system and the main three periods are Ones, Thousands, and Millions respectively. The main international units are the millions and the billions of the system. The separators are used to read place values by distinguishing and separating the three periods using commas. The first comma (or separator) in a number of International numeral systems is placed after the Hundreds place value post which the separators are marked after every three digits prevailing. For example, 123,445,789 is a number in the International numeral system.
| Periods | Place values | Number of symbols or digits |
|---|---|---|
| Millions | Hundred Millions | 9 |
| Ten Millions | 8 | |
| Millions | 7 | |
| Thousands | Hundred Thousands | 6 |
| Ten Thousands | 5 | |
| Thousands | 4 | |
| Ones | Hundreds | 3 |
| Tens | 2 | |
| Ones | 1 |
Things to Remember
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- Numeral systems are systems of numerations that are used for the expression of numbers in a consistent form using symbols or digits.
- Hindo - Arabic numeral system, originated in India is the positional decimal numeral system with a positional base of 10. It comprises 10 symbols or digits, that is, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- An ideal numeral system will be represented by a unique set of numbers having proper arithmetic and algebraic structure.
- Commas are used to separate periods in a number and help in reading place values of it. The commas are also called separators in the numeral system.
- The place value of a number is the numerical value of the digit in the number with reference to its position while the face value of a number is the digit itself. For example, the place value of 2 in 28 is 20 (since it is in the Tens position) while the face value of 2 in 28 is 2.
- The commonly used numeral systems in computers are the binary, octal, and hexadecimal number systems.
Also check: Place Value and Face Value
Sample Questions
Ques. What is meant by place value? Give an example. (2 Marks)
Ans. Place value is the positional numerical value of each symbol or digit in a number. It is used to read the expressed number. Each digit or symbol in a number has a fixed place value. For example, the place value of the digit 8 in the number 183 is 80 since it is in the Tens position while the place value of the digit 8 in the number 8,173 is 8,000 since it is in the Thousands position.
Ques. Find the place value of each digit in the number 38,450. (3 Marks)
Ans. Given, the number 38,450
There are a total of 5 digits in the number.
The place value of digit 0 in the number is Ones.
The place value of digit 5 in the number is Tens
The place value of digit 4 in the number is Hundreds
The place value of digit 8 in the number is Thousands
The place value of digit 3 in the number is Ten Thousands
Ques. Find the place value of the digit 9 in the number 798, 456. (3 Marks)
Ans. Given, the number 798, 456
There are a total of 6 digits in the number.
The place value of digit 6 in the number is Ones.
The place value of digit 5 in the number is Tens
The place value of digit 4 in the number is Hundreds
The place value of digit 8 in the number is Thousands
The place value of digit 9 in the number is Ten Thousands
The place value of digit 7 in the number is Hundred Thousands
Ques. Differentiate between the Indian Numeral System and the International Numeral System. (3 marks)
Ans.
| Indian Numeral System | International Numeral System |
|---|---|
| Nine place values are grouped into four periods, namely, Ones, Thousands, Lakhs, and Crores. | Nine place values are grouped into three periods, namely, Ones, Thousands, and Millions. |
| Separators are placed after the Hundreds value post which is marked after every 2 digits present. | Separators are placed after the Hundreds value post which is marked after every 3 digits present. |
| Place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores. | Place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, and Hundred Millions |
Ques. How will you rewrite the number 282829867 in the Indian numeral system and International numeral system using separators? (3 Marks)
Ans. In the Indian numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 2 digits present.
The number 282829867 in the Indian numeral system is rewritten as 28,28,29,867.
In the International numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 3 digits present.
The number 282829867 in the International numeral system is rewritten as 282,829,867.
Ques. Rewrite the number 8,84,96,779 from the Indian numeral system to the International numeral system. How do you read this number according to both systems? (3 Marks)
Ans. We have the number in the Indian numeral system as 8,84,96,779.
In the International numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 3 digits present.
Converting the number 8,84,96,779 to the International numeral system, we get the rewritten number as 88,496,779.
In the Indian numeral system, the number 8,84,96,779 is read as Eight Crore, EIghty-four Lakh, Ninety-six Thousand, Seven Hundred Seventy-nine.
In the International numeral system, the number 88,496,779 is read as Eighty-eight Million, Four Hundred Ninety-six Thousand, Seven Hundred Seventy-nine.
Ques. Rewrite the number 6,967,890 from the International numeral system to the Indian numeral system. How do you read this number according to the International numeral system? (3 Marks)
Ans. We have the number in the Indian numeral system as 6,967,890
In the Indian numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 2 digits present.
Converting the number 6,967,890 to the Indian numeral system, we get the rewritten number as 69,67,890.
In the Indian numeral system, the number 69,67,890.is read as Sixty-nine Lakh, Sixty-seven Thousand, Eight Hundred Ninety.
Ques. Find the number of zeroes present in one crore according to the Indian Numeral System. (3 Marks)
Ans. According to the Indian Numeral system, one crore is represented as 100 Lakhs, that is, 1 Crore=100 Lakh
Also, 1 Lakh=1,00,000
Hence, 1 Crore=100 (1,00,000), that is, 1 Crore=1,00,00,000
Therefore, the number of zeroes present in one crore is 7.
Ques. Rewrite the number 324567 in the Indian numeral system and the International numeral system. How do you read this number according to both systems?
Ans. In the Indian numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 2 digits present.
The number 324567 in the Indian numeral system is rewritten as 3,24,567. It is read as Three Lakh, Twenty-four Thousand, Five Hundred Sixty-seven.
In the International numeral system, the first comma (or separator) is placed after the Hundreds value post which is marked after every 3 digits present.
The number 324567 in the International numeral system is rewritten as 324,567. It is read as Three Hundred Twenty-four Thousand, Five Hundred Sixty-seven
Ques. Find the number of zeroes present in one million according to the International Numeral System. (2 Marks)
Ans. According to the International Numeral system, one million is represented as 1000 Thousand, that is, 1 Million=1000 Thousand
Also, 1 Thousand=1000
Hence, 1 Million=1000 (1000), that is, 1 Million=1,000,000
Therefore, the number of zeroes present in one million is 6.
Ques. Which numeral system does the number 38,45,689 belong to? Also, how do you read this number? (2 Marks)
Ans. The number 38,45,689 belongs to the Indian numeral system since the separators are first marked after the Hundreds value post which is further marked after every 2 digits.
The number 38,45,689 is read as Thirty-eight lakh, Forty-five Thousand, Six Hundred Eighty-nine.
Ques. Explain the significance of separators in the numeral system. (2 Marks)
Ans. Separators or commas are used to mark and distinguish different periods in a number. This marking of separators helps in reading the place values of the expressed number in a numeral system.
Ques. Which numeral system does the number 999,998,999 belong to? Also, how do you read this number? (2 Marks)
Ans. The number 999,998,999 belongs to the International numeral system since the separators are first marked after the Hundreds value post which is further marked after every 3 digits.
The number 999,998,999 is read as Nine Hundred Ninety-nine Million, Nine Hundred Ninety-eight Thousand, Nine Hundred Ninety-nine.
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