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Based on the content from the uploaded image, which explains 8-digit numbers and their expanded notation using the Indian numbering system, I have crafted some tough exam-style questions for your preparation.

### 1. **Understanding Large Numbers:**
   A company reported sales of 9,48,23,476 in a financial year.
   - (a) Write this number in words using the Indian numbering system.
   - (b) Provide the expanded notation for the number.

   **Answer:**
   - (a) Nine crore, forty-eight lakh, twenty-three thousand, four hundred seventy-six.
   - (b) Expanded notation:  
     \( 9,00,00,000 + 40,00,000 + 8,00,000 + 20,000 + 3,000 + 400 + 70 + 6 \)

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### 2. **Identifying Place Values:**
   What is the place value of the digit '6' in the number 5,67,89,234?
   - (a) What is the value of the digit '7'?
   - (b) Write the entire number in expanded notation.

   **Answer:**
   - (a) Place value of '6': 60,00,000 (6 million, or sixty lakh)
   - (b) Place value of '7': 7,00,000 (seven lakh)
   - Expanded notation:  
     \( 5,00,00,000 + 60,00,000 + 7,00,000 + 80,000 + 9,000 + 200 + 30 + 4 \)

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### 3. **Comparison of Large Numbers:**
   Compare the following two numbers and state which one is larger:
   - 4,52,36,789 and 5,23,46,987.
   - (a) Subtract the smaller number from the larger number.
   - (b) Express both numbers in words.

   **Answer:**
   - The larger number is 5,23,46,987.
   - (a) Subtraction: \( 5,23,46,987 - 4,52,36,789 = 71,10,198 \)
   - (b) 4,52,36,789: Four crore, fifty-two lakh, thirty-six thousand, seven hundred eighty-nine.  
     5,23,46,987: Five crore, twenty-three lakh, forty-six thousand, nine hundred eighty-seven.

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### 4. **Forming a Number with Given Digits:**
   Using the digits 3, 5, 8, 7, 2, 4, 6, and 9, form the largest possible 8-digit number. Write this number:
   - (a) In words using the Indian number system.
   - (b) In expanded notation.

   **Answer:**
   - (a) The largest possible number is 98,76,54,327.  
     In words: Ninety-eight crore, seventy-six lakh, fifty-four thousand, three hundred twenty-seven.
   - (b) Expanded notation:  
     \( 90,00,00,000 + 8,00,00,000 + 70,00,000 + 6,00,000 + 50,000 + 4,000 + 300 + 20 + 7 \)

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### 5. **Analyzing a Number Based on its Digits:**
   A number is written as 8,37,24,159.
   - (a) Identify the digits in the lakhs and crore places.
   - (b) If the digits in the lakhs and crore places are swapped, what will the new number be?
   - (c) Write the new number in expanded notation.

   **Answer:**
   - (a) Lakhs place digit: 3 (three lakh), Crores place digit: 8 (eight crore).
   - (b) Swapping these gives the new number: 3,87,24,159.
   - (c) Expanded notation:  
     \( 3,00,00,000 + 80,00,000 + 7,00,000 + 20,000 + 4,000 + 100 + 50 + 9 \)

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### Tip:
Always pay close attention to how commas are placed in large numbers when using the Indian numbering system. They help divide the number into crore, lakh, thousand, and smaller units for easier reading.

Do you want more details or have any questions on this topic? Here are some additional related questions to explore:

1. What is the place value of the digit '5' in 9,58,12,345?
2. How many zeros are there in one crore? Explain using the Indian numbering system.
3. Convert the number 7,89,46,213 to its international form and compare it with the Indian form.
4. Write 6,24,18,032 in expanded notation and then subtract 32 from it. What is the result?
5. If a number 5,00,00,000 is reduced by 47 lakh, what will be the new number?



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Prepare for exams with challenging questions based on 8-digit numbers, place values, and expanded notation using the Indian numbering system. Learn how to read large numbers and express them in words and expanded form. Suitable for students in Grades 4-6.

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