Indian Number System
Have you ever seen your parents read the newspaper and talk about numbers like "fifty lakhs" or "three crore"? These words - lakhs and crore - are part of the Indian Number System that we use every day in India. When your school announces that it collected Rs. 2,50,000 for a charity event, or when someone says India's population is about 140 crore, they are using the Indian Number System. This system tells us how to read, write, and organize large numbers using a special pattern of grouping digits. It uses place values like ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs, crore, and ten-crore. In this chapter, we will learn how the Indian Number System works, how to place commas correctly, and how to read any number written in this system. This is a very important part of the Knowing Our Numbers chapter in Grade 6 Maths because it forms the foundation for working with all large numbers.
What is Indian Number System - Grade 6 Maths (Knowing Our Numbers)?
The Indian Number System is the way we group and name large numbers in India. It is also called the Hindu-Arabic Number System because it was developed in ancient India.
In this system, we group digits into periods. A period is a group of digits separated by commas. The Indian system has the following periods:
Ones Period: This includes the Ones place, Tens place, and Hundreds place. This group has 3 digits.
Thousands Period: This includes the Thousands place and Ten-Thousands place. This group has 2 digits.
Lakhs Period: This includes the Lakhs place and Ten-Lakhs place. This group has 2 digits.
Crore Period: This includes the Crore place and Ten-Crore place. This group has 2 digits.
Here is the Indian Place Value Chart:
| Ten-Crore | Crore | Ten-Lakhs | Lakhs | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
| 10,00,00,000 | 1,00,00,000 | 10,00,000 | 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Notice the pattern of commas in the Indian system: after the first 3 digits from the right (ones period), we put a comma. Then we put a comma after every 2 digits. So a 7-digit number like 2345678 is written as 23,45,678.
This is different from the International system, which groups digits in threes. The Indian system is unique to India, Nepal, Sri Lanka, Bangladesh, Pakistan, and Myanmar.
Indian Number System Formula
The Indian Number System does not have a mathematical formula, but it has a pattern for placing commas and a place value chart that you should memorize.
Comma Placement Rule:
Step 1: Start from the rightmost digit (ones place).
Step 2: Count 3 digits from the right and place the first comma. This separates the Ones period (Hundreds, Tens, Ones).
Step 3: After that, place a comma after every 2 digits going left. Each group of 2 digits forms a period (Thousands, Lakhs, Crore).
Place Values (from right to left):
| Position | Name | Value |
| 1st | Ones | 1 |
| 2nd | Tens | 10 |
| 3rd | Hundreds | 100 |
| 4th | Thousands | 1,000 |
| 5th | Ten-Thousands | 10,000 |
| 6th | Lakhs | 1,00,000 |
| 7th | Ten-Lakhs | 10,00,000 |
| 8th | Crore | 1,00,00,000 |
| 9th | Ten-Crore | 10,00,00,000 |
Key relationships:
1 Thousand = 1,000 (10 Hundreds)
1 Lakh = 1,00,000 (100 Thousands)
1 Crore = 1,00,00,000 (100 Lakhs)
10 Crore = 10,00,00,000 (1,000 Lakhs)
Derivation and Proof
Let us understand how the Indian Number System builds up from the basics.
Start with the simplest idea: counting. 1, 2, 3, ..., 9. These are single-digit numbers.
When we reach 10, we need a new place - the tens place. Now we can count up to 99 using two digits.
At 100, we get the hundreds place. We can now represent numbers up to 999.
At 1,000, we move to the thousands place. Here is where the Indian system starts to differ from the International system. In the Indian system, the thousands period has only 2 places: Thousands and Ten-Thousands. So we count from 1,000 to 99,999 using 4 and 5 digit numbers.
At 1,00,000, we enter the lakhs. This is a uniquely Indian term. One lakh equals one hundred thousand. The lakhs period also has 2 places: Lakhs and Ten-Lakhs. So we count from 1,00,000 to 99,99,999.
At 1,00,00,000, we reach one crore. One crore equals one hundred lakhs, or ten million. Again, the crore period has 2 places: Crore and Ten-Crore.
Let us trace the number 5,34,26,819 through the chart:
| Ten-Crore | Crore | Ten-Lakhs | Lakhs | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
| - | 5 | 3 | 4 | 2 | 6 | 8 | 1 | 9 |
Reading: Five crore thirty-four lakh twenty-six thousand eight hundred and nineteen.
The beauty of this system is that each place value is exactly 10 times the place to its right. This base-10 structure makes arithmetic simple and consistent.
Types and Properties
Here are the different types of problems you will see related to the Indian Number System:
Type 1: Writing Numbers with Commas - You are given a number without commas and asked to write it with proper commas in the Indian system. Apply the comma placement rule: first comma after 3 digits from the right, then after every 2 digits.
Type 2: Reading Numbers in Words - You are given a number with commas and asked to write it in words. Read each period from left to right and say the period name. For example, 4,56,789 is read as "four lakh fifty-six thousand seven hundred and eighty-nine."
Type 3: Writing Numbers in Figures - The reverse of Type 2. You are given a number in words and asked to write it in digits. For example, "seven crore twelve lakh" = 7,12,00,000.
Type 4: Finding Place Value of a Digit - You are given a number and asked what the place value of a specific digit is. For example, in 3,45,678, the place value of 4 is 40,000 (four ten-thousands). Remember: place value = digit x value of its position.
Type 5: Expanded Form - Writing a number as the sum of each digit multiplied by its place value. For example, 2,34,567 = 2,00,000 + 30,000 + 4,000 + 500 + 60 + 7.
Type 6: Conversion Between Words and Numerals - Converting between Indian naming conventions (lakhs, crore) and numerals, which often involves understanding how many zeros each term represents.
Solved Examples
Example 1: Example 1: Placing Commas in Indian System
Problem: Write 34256789 using commas in the Indian Number System.
Solution:
Step 1: Start from the right. The first 3 digits are 789. Place a comma: ___789
Step 2: Next 2 digits: 56. Place a comma: __56,789
Step 3: Next 2 digits: 42. Place a comma: _42,56,789
Step 4: Remaining digits: 3. No more commas needed.
Answer: 3,42,56,789
This is read as: Three crore forty-two lakh fifty-six thousand seven hundred and eighty-nine.
Example 2: Example 2: Reading a Number in Words
Problem: Write the number 7,05,324 in words.
Solution:
Let us place the digits in the Indian place value chart:
| Lakhs | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
| 7 | 0 | 5 | 3 | 2 | 4 |
Reading from left to right:
7 in the Lakhs place = Seven lakh
0 in Ten-Thousands = (skip, since it is 0)
5 in Thousands = five thousand
3 in Hundreds = three hundred
24 = twenty-four
Answer: Seven lakh five thousand three hundred and twenty-four.
Example 3: Example 3: Writing a Number in Figures
Problem: Write in figures: Twelve crore seven lakh forty thousand and sixty-five.
Solution:
Twelve crore = 12,00,00,000
Seven lakh = 7,00,000
Forty thousand = 40,000
Sixty-five = 65
Adding them: 12,00,00,000 + 7,00,000 + 40,000 + 65 = 12,07,40,065
Answer: 12,07,40,065
Example 4: Example 4: Finding Place Value
Problem: In the number 8,35,641, find the place value of each digit.
Solution:
Let us write each digit with its position:
| Digit | Position | Place Value |
| 8 | Lakhs | 8 x 1,00,000 = 8,00,000 |
| 3 | Ten-Thousands | 3 x 10,000 = 30,000 |
| 5 | Thousands | 5 x 1,000 = 5,000 |
| 6 | Hundreds | 6 x 100 = 600 |
| 4 | Tens | 4 x 10 = 40 |
| 1 | Ones | 1 x 1 = 1 |
We can verify: 8,00,000 + 30,000 + 5,000 + 600 + 40 + 1 = 8,35,641. Correct!
Example 5: Example 5: Expanded Form
Problem: Write 4,02,538 in expanded form.
Solution:
4,02,538 = 4 x 1,00,000 + 0 x 10,000 + 2 x 1,000 + 5 x 100 + 3 x 10 + 8 x 1
= 4,00,000 + 0 + 2,000 + 500 + 30 + 8
= 4,00,000 + 2,000 + 500 + 30 + 8
Note: We skip the term with 0 since 0 x 10,000 = 0.
Example 6: Example 6: Face Value vs Place Value
Problem: Find the face value and place value of 6 in the number 3,64,521.
Solution:
The face value of a digit is the digit itself, regardless of its position.
Face value of 6 = 6
The place value depends on the position of the digit in the number.
In 3,64,521, the digit 6 is in the ten-thousands place.
Place value of 6 = 6 x 10,000 = 60,000
So the face value is 6 and the place value is 60,000. The place value is always much larger than the face value (unless the digit is in the ones place).
Example 7: Example 7: How Many Lakhs in a Crore?
Problem: How many lakhs make one crore?
Solution:
1 Crore = 1,00,00,000
1 Lakh = 1,00,000
Number of lakhs in a crore = 1,00,00,000 / 1,00,000 = 100
Therefore, 100 lakhs = 1 crore.
Similarly, 10 lakhs = 10,00,000 (ten lakh), and 100 lakhs = 1,00,00,000 (one crore).
Example 8: Example 8: Writing a Large Number
Problem: India's population is approximately 140 crore. Write this number in figures with commas in the Indian system.
Solution:
140 crore = 140 x 1,00,00,000
= 1,40,00,00,000
Let us verify the commas: Starting from right, first 3 digits: 000. Then groups of 2: 00, 00, 40, 1.
Answer: 1,40,00,00,000
This is read as: One hundred and forty crore, or one arab forty crore.
Example 9: Example 9: Converting Words to Number with Zeros
Problem: Write in figures: Nine lakh three hundred and seven.
Solution:
Nine lakh = 9,00,000
Three hundred and seven = 307
Total = 9,00,000 + 307 = 9,00,307
Notice that there are zeros in the ten-thousands and thousands places because there are no thousands in this number.
Answer: 9,00,307
Example 10: Example 10: Building Number from Place Values
Problem: A number has 3 in the crore place, 5 in the ten-lakhs place, 0 in the lakhs place, 2 in the ten-thousands place, 7 in the thousands place, 8 in the hundreds place, 1 in the tens place, and 4 in the ones place. Write the number.
Solution:
| Crore | Ten-Lakhs | Lakhs | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
| 3 | 5 | 0 | 2 | 7 | 8 | 1 | 4 |
Answer: 3,50,27,814
In words: Three crore fifty lakh twenty-seven thousand eight hundred and fourteen.
Real-World Applications
The Indian Number System is used everywhere in India and neighbouring countries. Every time you read a newspaper, watch the news, or see a price tag, you are using this system. It is deeply embedded in our daily life and language.
Government budgets are always announced in crore and lakh. When the Finance Minister says the education budget is Rs. 1,12,899 crore, understanding the Indian Number System helps you grasp the size of this amount. Bank statements, salary slips, property prices, and car prices all use lakhs and crore. If a car costs Rs. 8,50,000, you know it is eight lakh fifty thousand rupees. If a flat costs Rs. 1,20,00,000, you know it is one crore twenty lakh rupees.
In school, when you study geography, you learn that India's area is about 32,87,263 square kilometres. The height of Mount Everest is 8,849 metres. The length of the Ganges River is about 2,525 kilometres. In history, populations and revenues of empires are given in the Indian system. The Mughal Empire's revenue was measured in crore of rupees.
Cricket statistics use large numbers too. If someone says a player has earned Rs. 45 lakh from a tournament, you need to know the Indian system to understand that 45 lakh means Rs. 45,00,000. The total prize money for a cricket tournament might be Rs. 50 crore, which is Rs. 50,00,00,000. When a player is bought for Rs. 24.75 crore in the IPL auction, understanding lakhs and crore helps you appreciate the scale of these numbers.
In business, company revenues and profits are reported in crore. If a company has a revenue of Rs. 15,000 crore, that is Rs. 1,50,00,00,00,000. Share prices are in rupees, but market capitalisations are in lakh crore. Understanding these numbers is essential for financial literacy.
Even in everyday conversations, people say things like "that house costs 80 lakhs" or "the company made 5 crore profit." Your parents might discuss a fixed deposit of Rs. 10 lakh or a home loan of Rs. 50 lakh. Without understanding the Indian Number System, these numbers would be meaningless. The system makes it easy to talk about and understand large quantities because we group them in a way that is natural to our language and culture.
Key Points to Remember
- The Indian Number System groups digits into periods: Ones (3 digits), Thousands (2 digits), Lakhs (2 digits), Crore (2 digits).
- Commas are placed after the first 3 digits from the right, and then after every 2 digits.
- Key place values: Ones, Tens, Hundreds, Thousands, Ten-Thousands, Lakhs, Ten-Lakhs, Crore, Ten-Crore.
- 1 Lakh = 1,00,000 = 100 Thousands.
- 1 Crore = 1,00,00,000 = 100 Lakhs.
- Face value of a digit is the digit itself. Place value = digit x value of its position.
- Expanded form shows a number as the sum of each digit times its place value.
- When reading a number, go from left to right, reading each period and saying the period name.
- Zeros in a number mean there is nothing in that place, but they hold the position for other digits.
- The Indian system is used in India, Nepal, Bangladesh, Pakistan, Sri Lanka, and Myanmar.
Practice Problems
- Write 56789012 with commas in the Indian Number System.
- Write in words: 8,04,35,210.
- Write in figures: Twenty-three lakh sixty thousand and nine.
- Find the place value and face value of 7 in the number 5,71,20,346.
- Write the expanded form of 9,06,050.
- How many ten-thousands make one lakh?
- A school collected Rs. 3,25,750 for charity. Write this amount in words.
- Arrange in the Indian place value chart: 4,50,03,872. Read it in words.
Frequently Asked Questions
Q1. What is the difference between the Indian and International Number System?
The main difference is how digits are grouped. In the Indian system, after the first 3 digits from the right, digits are grouped in pairs (lakhs, crore). In the International system, digits are always grouped in threes (thousands, millions, billions). So 1,00,00,000 in the Indian system is written as 10,000,000 in the International system. The Indian system uses the terms lakh and crore, while the International system uses million and billion.
Q2. What is the largest number in the Indian Number System?
The Indian Number System can represent any number, no matter how large. There is no largest number. The commonly used place values go up to Ten-Crore (10,00,00,000 = Arab level), but you can extend further with Arab, Kharab, Neel, Padma, and Shankh. In practice, most numbers used in daily life go up to crore.
Q3. Why does the Indian system group differently than the International system?
The Indian Number System was developed based on the Indian languages, which have specific words for lakh (100 thousand) and crore (10 million). Since these words represent groups of 2 digits after the initial hundreds group, the comma placement follows this pattern. The International system groups in threes because words like thousand, million, billion each represent 3-digit groups.
Q4. What is the difference between face value and place value?
Face value is the digit itself, no matter where it appears in the number. Place value is the value of the digit based on its position. For example, in 5,43,267, the face value of 4 is 4, but its place value is 40,000 because 4 is in the ten-thousands place. Face value never changes, but place value depends on position.
Q5. How many zeros are in one lakh?
One lakh is written as 1,00,000. There are 5 zeros after the digit 1. Similarly, one crore (1,00,00,000) has 7 zeros, and ten crore (10,00,00,000) has 8 zeros.
Q6. What is the smallest 7-digit number in the Indian system?
The smallest 7-digit number is 10,00,000, which is read as ten lakh. The largest 6-digit number is 9,99,999. Adding 1 to 9,99,999 gives 10,00,000, making it the smallest 7-digit number.
Q7. How do I read a number with zeros in the middle?
When a number has zeros in the middle, you skip those places while reading. For example, 5,03,007 is read as five lakh three thousand and seven. You do not say 'zero ten-thousand' or 'zero hundred.' Just skip the zero positions and move to the next non-zero digit.
Q8. Is the Indian Number System used only in India?
No, the Indian Number System is also used in Nepal, Bangladesh, Pakistan, Sri Lanka, and Myanmar. These countries share a similar linguistic tradition and use the terms lakh and crore. However, for international business and scientific communication, the International Number System with millions and billions is used.
Q9. How do I convert lakhs to crore?
Since 1 crore = 100 lakhs, divide the number of lakhs by 100 to get crore. For example, 350 lakhs = 350 / 100 = 3.5 crore = 3 crore 50 lakh. To convert crore to lakhs, multiply by 100. For example, 7 crore = 7 x 100 = 700 lakhs.
Q10. Why is it important to place commas correctly?
Commas help us read large numbers easily. Without commas, 5342678 is hard to read. With commas in the Indian system (53,42,678), we can immediately see it is fifty-three lakh. Wrong comma placement can make you read the number incorrectly. For example, 5,342,678 (International style) would make you read it as five million, which is a different reading than the Indian way.
