Indian and International Number System (Grade 5)
There are two main systems for reading and writing large numbers: the Indian (Hindu-Arabic) number system and the International number system. Both systems use the same ten digits (0-9) and the same place value logic, but they group digits differently and use different period names.
In India, we say "five lakh" while the rest of the world says "five hundred thousand" for the same number. This is not just a language difference -- it reflects how the digits are grouped by commas. Learning both systems helps you read Indian newspapers, government reports, and also understand international data from websites, science journals, and global news.
In Class 5, you learn to write any number in both systems, convert between lakhs and millions, and understand why the same number looks different when commas are placed differently. This skill is increasingly important as students encounter global data through the internet and international competitions.
The core idea is simple: the digits of a number never change. Only the way we group them (using commas) and the names we give to those groups differ between the two systems.
What is Indian and International Number System - Class 5 Maths (Large Numbers)?
The Indian number system groups digits into periods of Ones (3 digits), Thousands (2 digits), Lakhs (2 digits), and Crores (2 digits). Commas are placed after the first three digits from the right, then after every two digits.
The International number system groups digits into periods of Ones (3 digits), Thousands (3 digits), Millions (3 digits), and Billions (3 digits). Commas are placed after every three digits from the right.
Side-by-side comparison:
| Value | Indian Name | Indian Notation | International Name | International Notation |
|---|---|---|---|---|
| 1 | One | 1 | One | 1 |
| 1,000 | One Thousand | 1,000 | One Thousand | 1,000 |
| 10,000 | Ten Thousand | 10,000 | Ten Thousand | 10,000 |
| 1,00,000 | One Lakh | 1,00,000 | Hundred Thousand | 100,000 |
| 10,00,000 | Ten Lakhs | 10,00,000 | One Million | 1,000,000 |
| 1,00,00,000 | One Crore | 1,00,00,000 | Ten Million | 10,000,000 |
| 1,00,00,00,000 | One Hundred Crore | 1,00,00,00,000 | One Billion | 1,000,000,000 |
Indian and International Number System (Grade 5) Formula
1 Lakh = 100 Thousand | 10 Lakhs = 1 Million
1 Crore = 10 Million | 100 Crores = 1 Billion
Quick conversion formulas:
- Lakhs to Millions: divide by 10. Example: 45 lakhs / 10 = 4.5 million.
- Millions to Lakhs: multiply by 10. Example: 3 million x 10 = 30 lakhs.
- Crores to Millions: multiply by 10. Example: 2 crores x 10 = 20 million.
- Millions to Crores: divide by 10. Example: 50 million / 10 = 5 crores.
Types and Properties
Comma placement rules -- the key difference:
| System | Comma Rule | Grouping Pattern | Example (same number) |
|---|---|---|---|
| Indian | First comma after 3 digits from right, then every 2 digits | ...2-2-2-3 | 23,45,678 |
| International | Comma after every 3 digits from right | ...3-3-3 | 2,345,678 |
Indian place value chart (up to crores):
| Period | Crores | Lakhs | Thousands | Ones | |||||
|---|---|---|---|---|---|---|---|---|---|
| Place | T.Cr | Cr | T.L | L | T.Th | Th | H | T | O |
| Value | 10Cr | 1Cr | 10L | 1L | 10Th | 1Th | 100 | 10 | 1 |
International place value chart (up to billions):
| Period | Millions | Thousands | Ones | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Place | H.M | T.M | M | H.Th | T.Th | Th | H | T | O |
| Value | 100M | 10M | 1M | 100Th | 10Th | 1Th | 100 | 10 | 1 |
Key observation: For numbers up to 99,999 (5 digits), both systems look identical because the first comma in both systems comes after 3 digits from the right. The difference begins only from 6-digit numbers onward.
Solved Examples
Example 1: Example 1: Write in Both Systems
Problem: Write the number 5834216 using commas in both the Indian and International systems.
Solution:
Indian system:
Step 1: Start from the right. First comma after 3 digits: 216.
Step 2: Then comma after every 2 digits: 34, then 58.
Step 3: Result: 58,34,216
Step 4: Number name: Fifty-eight lakh thirty-four thousand two hundred and sixteen.
International system:
Step 1: Start from the right. Comma after every 3 digits: 216, then 834, then 5.
Step 2: Result: 5,834,216
Step 3: Number name: Five million eight hundred thirty-four thousand two hundred sixteen.
Answer: Indian: 58,34,216 | International: 5,834,216
Example 2: Example 2: Read in Indian System
Problem: Read 4,07,560 in the Indian system.
Solution:
Step 1: Identify the periods by looking at the commas: 4 | 07 | 560
Step 2: Read each period:
- Lakhs period: 4 = Four lakh
- Thousands period: 07 = Seven thousand (the 0 in the ten-thousands place is not read)
- Ones period: 560 = Five hundred and sixty
Step 3: Combine: Four lakh seven thousand five hundred and sixty.
Answer: Four lakh seven thousand five hundred and sixty.
Example 3: Example 3: Read in International System
Problem: Read 407560 in the International system.
Solution:
Step 1: Place commas in the international style (every 3 digits from right): 407,560.
Step 2: Read each period:
- Thousands period: 407 = Four hundred seven thousand
- Ones period: 560 = Five hundred sixty
Step 3: Combine: Four hundred seven thousand five hundred sixty.
Answer: Four hundred seven thousand five hundred sixty.
Note: The same number (407560) has different names in the two systems: "Four lakh seven thousand..." (Indian) vs "Four hundred seven thousand..." (International). The value is identical.
Example 4: Example 4: Convert Lakhs to Millions
Problem: Express 35 lakhs in the international system.
Solution:
Step 1: Write 35 lakhs in figures: 35,00,000 (Indian notation).
Step 2: Use the conversion: 10 lakhs = 1 million.
Step 3: 35 lakhs = 35 / 10 = 3.5 million.
Step 4: In international figures: 3,500,000.
Verification: Both represent the same number -- 3500000.
Answer: 35 lakhs = 3.5 million or 3,500,000
Example 5: Example 5: Convert Millions to Lakhs
Problem: A global report says a city has 2.7 million people. Express this in the Indian system.
Solution:
Step 1: Use the conversion: 1 million = 10 lakhs.
Step 2: 2.7 million = 2.7 x 10 = 27 lakhs.
Step 3: In Indian figures: 27,00,000.
Verification: 27,00,000 in international notation = 2,700,000 = 2.7 million. Correct.
Answer: 2.7 million = 27 lakhs or 27,00,000
Example 6: Example 6: Place the Commas for an 8-Digit Number
Problem: Write 13254089 with commas in both systems and read in both.
Solution:
Indian system:
- From right: 089 (ones period), 54 (thousands), 32 (lakhs), 1 (crores)
- Result: 1,32,54,089
- Name: One crore thirty-two lakh fifty-four thousand and eighty-nine.
International system:
- From right: 089 (ones), 254 (thousands), 13 (millions)
- Result: 13,254,089
- Name: Thirteen million two hundred fifty-four thousand eighty-nine.
Answer: Indian: 1,32,54,089 | International: 13,254,089
Example 7: Example 7: When Both Systems Look the Same
Problem: Priya read that India's tiger population is about 3,682. Aman read a global report saying there are 4,500 tigers worldwide. Are these numbers written in the Indian or International system?
Solution:
Step 1: Both numbers (3,682 and 4,500) are 4-digit numbers.
Step 2: For numbers up to 99,999, both the Indian and International systems place commas the same way -- after the first 3 digits from the right.
Step 3: So 3,682 and 4,500 look identical in both systems.
Answer: Both numbers look the same in either system. The two systems produce different-looking numbers only for numbers with 6 or more digits.
Example 8: Example 8: Fill the Conversion Table
Problem: Complete the table for the number 72,50,000.
Solution:
| Property | Indian System | International System |
|---|---|---|
| With commas | 72,50,000 | 7,250,000 |
| Number name | Seventy-two lakh fifty thousand | Seven million two hundred fifty thousand |
| Period breakdown | 72 lakhs + 50 thousands | 7 millions + 250 thousands |
Answer: Same value, different grouping and naming.
Example 9: Example 9: Real-Life Application
Problem: The cost of a flat in Bangalore is ₹85,00,000. Express this in the international system and in millions.
Solution:
Step 1: ₹85,00,000 means 85 lakhs in the Indian system.
Step 2: Place commas in international style: ₹8,500,000.
Step 3: Convert: 85 lakhs / 10 = 8.5 million.
Step 4: So the flat costs eight million five hundred thousand rupees.
Answer: ₹85,00,000 = ₹8,500,000 = 8.5 million rupees.
Example 10: Example 10: Converting Crores to Millions
Problem: The annual budget of a school chain is ₹12 crores. Express this in millions.
Solution:
Step 1: 1 crore = 10 million.
Step 2: 12 crores = 12 x 10 = 120 million.
Step 3: In figures: 12,00,00,000 (Indian) = 120,000,000 (International).
Verification: Count the digits in both: 9 digits. Both represent 12 followed by 7 zeros. Correct.
Answer: 12 crores = 120 million.
Real-World Applications
Knowing both number systems is essential in the modern world:
- Reading Indian newspapers: "India's population is 140 crore" -- you must understand crores.
- Reading international news: "Apple is worth $3 trillion" -- you must understand trillions and billions.
- Travel and currency exchange: International prices are in millions, not lakhs.
- Science and technology: Scientific data and computer storage (MB, GB) use the international system.
- Banking: International wire transfers and forex statements use millions and billions.
- Government budgets: India's annual budget is expressed in crores, but the same data on international platforms appears in billions.
- Competitive exams: Questions often ask students to convert between the two systems.
Key Points to Remember
- The Indian system uses periods: Ones (3 digits), Thousands (2 digits), Lakhs (2 digits), Crores (2 digits). Commas: 3-2-2-2 from the right.
- The International system uses periods: Ones (3 digits), Thousands (3 digits), Millions (3 digits), Billions (3 digits). Commas: 3-3-3 from the right.
- 1 Lakh = 100 Thousand (same value, different names).
- 10 Lakhs = 1 Million.
- 1 Crore = 10 Million.
- 100 Crores = 1 Billion.
- For numbers up to 99,999 (5 digits), both systems look and sound identical.
- The difference in comma placement and period names starts from 6-digit numbers onward.
- The digits and their order never change between systems -- only the comma placement and the names of the groups differ.
- To convert lakhs to millions, divide by 10. To convert millions to lakhs, multiply by 10.
Practice Problems
- Write 9463520 with commas in both the Indian and International systems. Read the number in both systems.
- Read 36,80,000 in the Indian system and rewrite it in the International system with commas.
- Convert 4.2 million to lakhs. Write the result in Indian notation.
- Write the number name of 2,05,00,000 in both the Indian and International systems.
- A school has 1,25,000 students. Write this in the International system and express it in thousands.
- Express 50 crores in millions. How many billions is that?
- Place commas correctly in the number 804700210 using both systems. Write the number name in each.
- Aditi's grandfather says his farm is worth ₹1.5 crore. How many millions of rupees is that? Write it in international notation.
Frequently Asked Questions
Q1. What is the main difference between the Indian and International number systems?
The main difference is in how digits are grouped by commas. The Indian system groups as 3-2-2 from the right (Ones, Thousands, Lakhs, Crores). The International system groups as 3-3-3 from the right (Ones, Thousands, Millions). The actual number value stays exactly the same -- only the notation and names differ.
Q2. How many lakhs make 1 million?
10 lakhs = 1 million. Both equal 10,00,000 (Indian) or 1,000,000 (International). So if something costs 25 lakhs, it costs 2.5 million.
Q3. How many crores make 1 billion?
100 crores = 1 billion. So 1 billion = 1,00,00,00,000 in the Indian system. India's population of about 140 crores equals 1.4 billion.
Q4. Why does India use a different number system from the rest of the world?
The Indian number system (lakhs, crores) originated from ancient Indian mathematics and has been used for thousands of years in the subcontinent. It aligns naturally with how numbers are spoken in Hindi, Tamil, Bengali, and other Indian languages. The international system developed separately in Western countries.
Q5. Where do we see the international system used in India?
The international system appears in Indian science textbooks, IT companies, international trade documents, and global news. For example, phrases like "India's GDP is $3.7 trillion" or "a 256 GB storage device" use the international system.
Q6. Do the digits of a number change when we switch between the two systems?
No. The digits and their sequence remain exactly the same. Only the comma placement and the period names change. The number 5834216 is written as 58,34,216 (Indian) or 5,834,216 (International), but the digit sequence 5-8-3-4-2-1-6 does not change.
Q7. At what point do the two systems start looking different?
The two systems look identical for numbers up to 5 digits (99,999). The difference begins at 6-digit numbers: 1,00,000 (Indian) vs 100,000 (International). Below 6 digits, both systems place a single comma after the first 3 digits from the right.
Q8. How do I quickly convert lakhs to millions and vice versa?
Lakhs to millions: divide by 10 (e.g., 45 lakhs / 10 = 4.5 million). Millions to lakhs: multiply by 10 (e.g., 3 million x 10 = 30 lakhs). For crores and millions: 1 crore = 10 million.
Q9. Is this topic part of the NCERT Class 5 syllabus?
Yes. The NCERT Class 5 Maths textbook introduces the comparison between Indian and International number systems as part of the chapter on large numbers. Students are expected to read and write numbers in both systems and convert between lakhs/crores and millions/billions.
Q10. Which system should I use in exams?
Use the system specified in the question. If the question says "write in the Indian system," use lakhs and crores with Indian comma placement. If it says "International system," use millions with international commas. If not specified, CBSE exams typically expect the Indian system.
Related Topics
- Place Value of Large Numbers
- Indian Number System
- Numbers up to Lakhs
- Reading and Writing Large Numbers
- Comparing Large Numbers (Grade 5)
- Ordering Large Numbers (Grade 5)
- Rounding Large Numbers
- Estimation (Grade 5)
- Roman Numerals (I to M)
- Numbers up to Crores
- Number Names in Lakhs and Crores
- Expanded Form of Large Numbers
