Did you know? When the mathematics problems are solved, the focus is on the math techniques and the answer itself, but here we seem to give less importance to the place value of numbers and the usage of commas. So, here we will know the importance of place value both in the case of math and in real life and the differences between two types of place value systems with conversions, easy solved examples and FAQS. Here, we will learn about 1 billion in rupees conversion.

Place value system 

Back in the ancient and olden days, there was no one standard number system to represent numbers; instead, the numbers were represented or counted with the help of rocks, sticks and pebbles. So, later the various standard number systems were invented along with place value systems. The number system is a method of representing numbers which are also known as the enumeration scheme.

There are two types of place value systems, namely:

• The Indian Place Value System
• The International Place Value System

Indian place value system 

In the Indian place value system, four periods consist of various places, and this system is also referred to as the Hindu-Arabic system of numeration. The four periods are ones, thousands, lakhs, crores. 

Below we will see the Indian place value chart with periods, places and shortcuts for places. The main important thing to note is that the periods are read for numbers from right to left. Also, commas in the Indian system starts from hundreds and is later on used for every two numbers. 

For example, let’s take the number 10,350. By reading from right to left, 350 is in the one place, and 10 is in the thousands place. You will clearly understand once the place value chart is drawn. Refer below for the chart.

INDIAN PLACE VALUE CHART
PERIODS	PLACES	DENOTED BY
CRORES	TEN CRORES 10,00,00,000	TC
	CRORES 1,00,00,000	C
LAKHS	TEN LAKHS 10,00,000	TL
	LAKHS 1,00,000	L
THOUSANDS	TEN THOUSAND 10,000	T-TH
	THOUSANDS 1,000	TH
ONES	HUNDREDS 100	H
	TENS 10	T
	ONES 1	O

From the above chart, we can understand how periods are divided into places and how shortcuts for simple and easy understanding denote these places. Now let’s understand how the Indian place-value system works through a simple example:

Let’s take a random number; 

123456789

The place value from right to left, which is from 9 to 1, can be interpreted as 

• 9 is in the one’s position
• 8 is in the tens position
• 7 is in the hundreds position
• 6 is in the thousands position
• 5 is in the ten thousand position
• 4 is in the lakhs position
• 3 is in the ten lakhs position
• 2 is in the crores position
• 1 is in the ten crores position

And the usage of commas in the Indian place-value system for the above example 123456789 is – 12,34,56,789.

International place value system

In the international place value system, three periods consist of 3 places, each equal to a total of 9 places. Also, the comma usage starts from hundreds of places and is later used for every three numbers.

INTERNATIONAL PLACE VALUE CHART
PERIODS	PLACES	DENOTED BY
MILLIONS	HUNDRED MILLION 100,000,000	HM
	TEN MILLION 10,000,000	TM
	MILLIONS 1,000,000	M
THOUSANDS	HUNDRED THOUSAND 100,000	H-TH
	TEN THOUSAND 10,000	T-TH
	THOUSAND 1,000	TH
ONES	HUNDRED 100	H
	TENS 10	T
	ONES 1	O

From the above chart, we can understand how each period is divided into places. Now let’s take an example of how the international system works 

Let’s take an example of a random number same as taken above to understand easily

123456789

The place value from right to left, which is from 9 to 1, can be interpreted as 

• 9 is in the one’s place
• 8 is in the tens place
• 7 is in the hundreds place
• 6 is in the thousands place
• 5 is in the ten thousand place
• 4 is in the hundred thousand place
• 3 is in the millions place
• 2 is in the ten million place
• 1 is in the hundred million places.

And the usage of commas in the international place value system for the above example 123456789 is – 123,456,789. 

Comparison between Indian and international place value systems

The following important points can be drawn from both the place value systems:

• If you thoroughly observe, one thing can be found out that up to 5 place values from both the systems, which is from right to left, are the same, and the difference only starts after the 5th place value, which is from the 6th place
• So the difference from 6th place for both the systems looks like

1 lakh = 100 thousand

10 lakhs = 1 million

1 crore = 10 million

10 crores = 100 million

• The international place value system can also be included by the billions period and for the students who like to challenge themselves and upgrade their skills can learn converting large numbers and practice getting the deep understanding of the place value system and conversion from billions to rupees.

What is the face value?

The particular number or digit’s face value is the number itself. And the place value can be obtained by multiplying the digit’s face value with its place value. For example, let’s take a number which is:

123456789

For this, let’s try to calculate both place value and face value 

The number 5 face value is 5 itself, and the place value is 5  10,000 = 50,000 (5 ten thousand)

Also let’s take another number which is 2 and face value for 2 is 2 itself and place value is 210,000,000 = 20,000,000 (2 ten millions or 2 crores).

So, for the remaining numbers, you can practice or test yourself for practical understanding.

And the place value for decimals can look like tenths, hundredths, and thousandths and so on from left to right and not from right to left since these are decimals and not numbers.

Importance of place value system in math and real life

Place value helps in laying the foundation for multiple digit multiplication, decimal system. In real life, it helps in making decisions regarding time, distance, weight and costs. And for most of the mathematical concepts, grasping depends on the understanding of place value.

For example, let’s take a number of 1,50,00,00,000 which can also be written as 15 108. Place value system helps both in expanding and writing to the power of many numbers and equations.

Frequently asked questions (faqs)

1. What is the difference between comma usage for Indian and international place value systems?

In both the systems, the usage of comma starts from hundreds from right to left and then in the Indian system, the comma is used for every 2 numbers and in the international system for every 3 numbers.

2. What is the difference between face value and place value?

The face value of the digit is the digit itself, and the place value is obtained by the multiplication of the digit’s face value with its place value.

3. What are 1 billion conversions in rupees?

1 billion = 1,000,000,000 in international system

1 billion = 1,00,00,00,000 (100 crores) in the Indian system.

Conclusion

Since now we know about both Indian and international place value systems and the importance of place value, from now on, all mathematics concepts will be easily understandable with the logic behind them. For more understanding of the conceptual area, you can practice some practical problems.