Number System
In ancient times, people used primitive methods for counting things. This trend continued for a long time as the transactions were based on the exchange of goods to goods. But in the course of development, it became very difficult for you to do things in huge. Hence, the need for calculation of things became the need of an hour and in due process, the system of numbers came into existence. We have various types of number systems across various countries of the world based on their language.
A number system is a method of representing numbers. It is also known as the enumeration scheme, which determines a set of values to describe a quantity. The position of a digit in a number determines the value of the digit in it. For instance, 5 in 350 represents 5 tens, or 50; but 5 in 5,006 represents 5,000. Kids need to know that while the same digit can be present in many numbers, its value depends on where it is in the number.
Example
In the number 1329:
1 holds the thousands position.
3 holds the hundreds position.
2 holds the tens position.
9 holds the position of the one.
More on Place Value
Whole numbers are arranged in groups of three, called periods. Each period features a hundred(s), ten(s), and one(s) position.
Number 123 456 789 is below as an example. Here, 8 holds the tens position, 5 holds the ten-thousands position, and so on.
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Decimal numbers are also organized in groups of three called periods. Each period features a ten(th), hundred(th), and thousand(th) position as explained in the below example.
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Place Value and the Face Value
The digit's place value is the product of the digit's face value and its place value, while a digit's face value is the digit itself.
In this example, we will calculate the face value and place a value of 6 in 6,45,100.
The face value of 6 in 6,45,100 is ‘6’.
The place value of the digit is obtained by multiplying the face value of the digit and the value of its place, so, the place value of 6 in 6,45,100 is 6 x 1,00,000 = 6,00,000 (6 Lakh).
Expanded Notation
We express each digit of a number to its position value in an extended form. Let's see the extended 29,1233 number notation.
In three different ways, this can be expanded:
1. 2 ten thousand + 9 thousand + 1 hundreds + 2 tens + 3 ones
2. (2 x 10,000) + (9 x 1,000) + (1 x 100) + (2 x 10) + (3 x 1)
3. 20000 + 9000 + 100 + 20 + 3
The standard form of 60000+4000+40+6 is 64,046.
The Indian System and the International System
Indian System:
The first period, consisting of three place values (ones, tens, and hundreds), is one in the Indian system of numeration, starting from the right. There are thousands in the next period, consisting of two-position values (thousands and ten thousand). Lakhs, consisting of two-position values (lakhs and ten lakhs), and then crores, and so on is the third cycle from the right. This enumeration scheme is often referred to as the Hindu-Arabic system of numeration. To divide the cycles, we use commas, which help us read and write large numbers. The first comma comes from the right after three digits (i.e., after one period) in the Indian scheme, and the next comma comes after the next two digits (i.e., after the thousand periods) and then after every two digits, and so on.
Indian Place Value Chart
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Consider an example of the International Numeration System:
In the Indian numeration scheme,
92357385 = 9,23,57,3855
Likewise, 2930625 will be translated as 29,30,625 in the Indian method of numeration.
The first cycle, consisting of three place values (ones, tens, and hundreds), is one in the International Numeration Scheme, beginning from the right. Thousands belong to the next period, consisting of three place values (one thousand, ten thousand, and one hundred thousand) and then millions and then billions.
International Place Value Chart
Comparison of Two Number Systems:
Comparison Between Indian and International Numeral System
If we compare both systems, we can come to the conclusion below.
100 thousand = 1 lakh
1 million = 10 lakhs
10 million = 1 crore
100 millions = 10 crores
FAQs on Place Value
1. How to Make a Place Value Chart?
To form an Indian place value chart, draw 4 columns showing the 4 periods: ones, thousands, lakhs, and crores. Draw sub-columns for each time to display various position values: ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores.
Similarly, draw 3 columns representing the 3 periods: ones, thousands, and millions, to create an International Place Value Map. Draw sub-columns for each time to display the different values of the place: ones, tens, hundreds, thousands, ten thousand, hundreds of thousands, millions, ten million, hundreds of millions.
For example, the number 26984 is regarded in the Indian place value chart as follows.
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2. Explain value and place value with the help of an example?
The place value of a digit can be defined based on its location in the number as the value expressed by the digit in a number. The place value of tens is 10 times the digit for a two-digit number; for example, the place value of 5 in number 57 is 5 x 10 = 50, and the place value of one digit is 7 x 1 = 7. Similarly, in a three-digit number, the place value for hundreds of digits is 100 x the face value of the digit. In the same way, the values forward as the same.
3. How the Indian and International numeral systems are different?
The main difference between the Indian and International numeral systems is the placement of commas (separator). In the Indian system lakhs and in the international system millions are replaced after thousands.
4. Why is it essential to learn the place value system during the primary level of education?
Place values are the basis for knowing numbers, their position, and their values. They are also helpful to learn the basics of long multiplication, addition, and subtraction. Place value allows the student learning scientific notation to understand why 69,800,000 can be represented as 6.98 X 107.