[Maths Class Notes] on Place Value Pdf for Exam

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