Numbers up to Crores
In Class 5, students extend their understanding of the number system from lakhs to crores. The Indian number system uses periods — Ones, Thousands, Lakhs, and Crores — to organise large numbers. Learning to read, write, and work with numbers up to crores is essential for understanding population figures, distances in geography, and financial data.
A crore equals 100 lakhs or 1,00,00,000 (one followed by seven zeroes). Numbers in this range have 7, 8, or 9 digits. By mastering place value in the crores period, students can read any number used in everyday Indian life — from city populations to government budgets.
What is Numbers up to Crores - Class 5 Maths (Large Numbers)?
A number is said to be in crores when its value reaches or exceeds 1,00,00,000 (one crore). In the Indian place value system, the places from right to left are:
| Crores Period | Lakhs Period | Thousands Period | Ones Period |
|---|---|---|---|
| Ten Crores (TC) | Crores (C) | Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
Place values:
- Ones = 1
- Tens = 10
- Hundreds = 100
- Thousands = 1,000
- Ten Thousands = 10,000
- Lakhs = 1,00,000
- Ten Lakhs = 10,00,000
- Crores = 1,00,00,000
- Ten Crores = 10,00,00,000
The comma placement in the Indian system follows the pattern: after the first 3 digits from the right, then every 2 digits. For example: 5,27,63,148 (five crore twenty-seven lakh sixty-three thousand one hundred forty-eight).
Numbers up to Crores Formula
1 Crore = 100 Lakhs = 1,00,00,000
1 Ten Crore = 10 Crores = 10,00,00,000
To find the place value of a digit: multiply the digit by the value of its place.
To find the face value of a digit: it is simply the digit itself, regardless of its position.
Types and Properties
Numbers up to crores can be classified by the number of digits:
- 7-digit numbers: Range from 10,00,001 to 99,99,999 (Ten Lakhs to just below one crore)
- 8-digit numbers: Range from 1,00,00,000 to 9,99,99,999 (One Crore to just below ten crores)
- 9-digit numbers: Range from 10,00,00,000 to 99,99,99,999 (Ten Crores to just below one arab)
Indian System vs International System:
| Indian System | International System |
|---|---|
| 1,00,000 (One Lakh) | 100,000 (Hundred Thousand) |
| 10,00,000 (Ten Lakhs) | 1,000,000 (One Million) |
| 1,00,00,000 (One Crore) | 10,000,000 (Ten Million) |
| 10,00,00,000 (Ten Crores) | 100,000,000 (Hundred Million) |
Solved Examples
Example 1: Example 1: Reading a 7-digit number
Problem: Write the number name for 34,56,789 in the Indian system.
Solution:
Step 1: Identify the periods using commas — 34,56,789.
Step 2: 34 lakh, 56 thousand, 789.
Step 3: Read: Thirty-four lakh fifty-six thousand seven hundred eighty-nine.
Answer: Thirty-four lakh fifty-six thousand seven hundred eighty-nine
Example 2: Example 2: Writing an 8-digit number in figures
Problem: Write in figures: Five crore twelve lakh thirty-four thousand five hundred sixty-seven.
Solution:
Step 1: Crores place = 5 → 5,_ _,_ _,_ _ _
Step 2: Lakhs place = 12 → 5,12,_ _,_ _ _
Step 3: Thousands place = 34 → 5,12,34,_ _ _
Step 4: Ones place = 567 → 5,12,34,567
Answer: 5,12,34,567
Example 3: Example 3: Place value vs face value
Problem: In the number 7,35,62,148, find the place value and face value of 3.
Solution:
Step 1: Write the place value chart:
| C | TL | L | TTh | Th | H | T | O |
|---|---|---|---|---|---|---|---|
| 7 | 3 | 5 | 6 | 2 | 1 | 4 | 8 |
Step 2: The digit 3 is in the Ten Lakhs place.
Step 3: Place value = 3 × 10,00,000 = 30,00,000
Step 4: Face value = 3
Answer: Place value = 30,00,000; Face value = 3
Example 4: Example 4: Expanded form of a number in crores
Problem: Write the expanded form of 2,45,13,086.
Solution:
Step 1: Identify each digit's place value:
- 2 × 1,00,00,000 = 2,00,00,000
- 4 × 10,00,000 = 40,00,000
- 5 × 1,00,000 = 5,00,000
- 1 × 10,000 = 10,000
- 3 × 1,000 = 3,000
- 0 × 100 = 0
- 8 × 10 = 80
- 6 × 1 = 6
Answer: 2,45,13,086 = 2,00,00,000 + 40,00,000 + 5,00,000 + 10,000 + 3,000 + 80 + 6
Example 5: Example 5: Comparing 8-digit numbers
Problem: Compare 4,72,31,560 and 4,72,35,102. Which is greater?
Solution:
Step 1: Both are 8-digit numbers, so compare digit by digit from left.
Step 2: Crores digit: 4 = 4 (same)
Step 3: Ten Lakhs digit: 7 = 7 (same)
Step 4: Lakhs digit: 2 = 2 (same)
Step 5: Ten Thousands digit: 3 = 3 (same)
Step 6: Thousands digit: 1 < 5
Answer: 4,72,31,560 < 4,72,35,102
Example 6: Example 6: Forming the largest 8-digit number
Problem: Using the digits 3, 0, 7, 5, 1, 9, 2, 8, form the largest 8-digit number.
Solution:
Step 1: Arrange the digits in descending order: 9, 8, 7, 5, 3, 2, 1, 0.
Step 2: Write them together: 9,87,53,210.
Answer: The largest 8-digit number is 9,87,53,210
Example 7: Example 7: Word problem — Population
Problem: The population of City A is 1,25,34,000 and City B is 98,76,000. What is the total population of both cities?
Solution:
Step 1: Write the numbers: 1,25,34,000 + 98,76,000
Step 2: Add:
1,25,34,000
+ 98,76,000
-----------
2,24,10,000
Answer: The total population is 2,24,10,000 (Two crore twenty-four lakh ten thousand)
Example 8: Example 8: Converting between Indian and International systems
Problem: Express 3,50,00,000 in the International system.
Solution:
Step 1: In the Indian system: 3,50,00,000 = 3 crore 50 lakh.
Step 2: 1 crore = 10 million, so 3 crore = 30 million.
Step 3: 50 lakh = 5 million.
Step 4: Total = 30 million + 5 million = 35 million.
Step 5: In International notation: 35,000,000.
Answer: 3,50,00,000 = 35,000,000 (thirty-five million)
Example 9: Example 9: Predecessor and successor of a crore number
Problem: Find the predecessor and successor of 5,00,00,000.
Solution:
Step 1: Predecessor = 5,00,00,000 − 1 = 4,99,99,999
Step 2: Successor = 5,00,00,000 + 1 = 5,00,00,001
Answer: Predecessor = 4,99,99,999; Successor = 5,00,00,001
Example 10: Example 10: Rounding to the nearest crore
Problem: Round 3,67,45,000 to the nearest crore.
Solution:
Step 1: The crores digit is 3. The digit to its right (ten lakhs) is 6.
Step 2: Since 6 ≥ 5, round up the crores digit: 3 → 4.
Step 3: Replace all digits after crores with 0.
Answer: 3,67,45,000 rounded to the nearest crore = 4,00,00,000
Real-World Applications
Numbers in crores appear frequently in everyday Indian life:
- Population data: India's population is expressed in crores (e.g., approximately 142 crore people).
- Government budgets: Union Budget allocations are in crores of rupees (e.g., ₹5,00,000 crore for education).
- Banking and finance: Large transactions, company revenues, and GDP figures use crores.
- Geography: Distances between planets, areas of countries in square kilometres are expressed in large numbers.
- Cricket: IPL auction prices, stadium capacities, and viewership numbers often reach crores.
Key Points to Remember
- 1 crore = 100 lakhs = 1,00,00,000 (7 zeroes after 1).
- 1 ten crore = 10 crores = 10,00,00,000 (8 zeroes after 1).
- In the Indian system, commas are placed after the first 3 digits from the right, then after every 2 digits.
- The place value of a digit depends on its position; the face value is the digit itself.
- To compare numbers with the same number of digits, compare digit by digit from the leftmost place.
- A number with more digits is always greater than a number with fewer digits.
- 1 crore in the International system = 10 million.
- The successor of a number is obtained by adding 1; the predecessor by subtracting 1.
Practice Problems
- Write the number name for 6,38,04,215 in the Indian system.
- Write in figures: Eight crore seventy-two lakh nine thousand three hundred forty-one.
- Find the place value of 5 in the number 5,04,23,867.
- Write the expanded form of 9,12,30,405.
- Arrange in ascending order: 3,45,67,890; 3,45,76,098; 3,45,67,809.
- The annual income of a company is ₹12,45,00,000. Express this amount in the International system.
- Form the smallest 9-digit number using the digits 4, 0, 2, 7, 1, 8, 3, 5, 6 (use each digit once).
- Find the difference between the place value and face value of 7 in 2,73,56,481.
Frequently Asked Questions
Q1. What is 1 crore in numbers?
1 crore is written as 1,00,00,000 in the Indian system. It has 7 zeroes after the digit 1 and equals 100 lakhs or 10 million in the International system.
Q2. How many zeroes does 1 crore have?
1 crore has 7 zeroes. Written out: 1,00,00,000. Similarly, 10 crores has 8 zeroes (10,00,00,000).
Q3. What is the difference between the Indian and International number system?
The Indian system groups digits in periods of 2 (after the initial 3) and uses terms like lakh and crore. The International system groups digits in periods of 3 and uses million and billion. For example, 1 crore = 10 million.
Q4. How do you place commas in the Indian system?
Place the first comma after 3 digits from the right (hundreds), then a comma after every 2 digits. Example: 5,23,45,678 — the commas separate crores, lakhs, thousands, and hundreds.
Q5. What comes after crores in the Indian number system?
After crores come ten crores, then arab (1,00,00,00,000 = 100 crores). However, in the Class 5 NCERT syllabus, numbers are studied up to ten crores.
Q6. How do you compare two numbers in crores?
First check the number of digits — more digits means a larger number. If both have the same number of digits, compare digit by digit starting from the leftmost position until you find a difference.
Q7. What is the smallest 8-digit number?
The smallest 8-digit number is 1,00,00,000 (one crore). The largest 7-digit number is 99,99,999, and adding 1 gives the smallest 8-digit number.
Q8. Is this topic covered in the NCERT Class 5 Maths textbook?
Yes. Numbers up to crores is part of the Large Numbers chapter in Class 5 NCERT Maths. Students learn place value, reading, writing, comparing, and basic operations with numbers up to crores.
Q9. How is the place value of a digit different from its face value?
The face value of a digit is the digit itself (e.g., face value of 5 is always 5). The place value depends on the digit's position (e.g., 5 in the lakhs place has a place value of 5,00,000).
Related Topics
- Numbers up to Lakhs
- Place Value of Large Numbers
- Indian and International Number System (Grade 5)
- 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)
- Number Names in Lakhs and Crores
- Expanded Form of Large Numbers
- Predecessor and Successor (Grade 5)
