Based on the image content, which covers the topic of 8-digit numbers (crores), here are five challenging questions to test deeper understanding:

1. Expanded Notation Challenge:

Write the expanded notation for the number 4,58,18,987. Explain the place values for each digit in the number.

Answer:
The expanded notation for 4,58,18,987 is:
$4 \times 1,00,00,000 + 5 \times 10,00,000 + 8 \times 1,00,000 + 1 \times 10,000 + 8 \times 1,000 + 9 \times 100 + 8 \times 10 + 7 \times 1$.
This can be written as:
$4,00,00,000 + 50,00,000 + 8,00,000 + 10,000 + 8,000 + 900 + 80 + 7$.

2. Place Value and Comma Placement:

A number is written as 5,63,45,271.
(a) Identify the place value of the digit 3.
(b) Explain the significance of comma placement in large numbers as per the Indian number system.

Answer:
(a) The digit 3 is in the lakhs place, so its place value is 3,00,000.
(b) In the Indian number system, commas are placed after every two digits starting from the right, following the thousand period, lakh period, and crore period. For example, in 5,63,45,271, the first comma separates the thousands period, the second separates the lakhs period, and the third separates the crores period.

3. Comparison and Word Form:

Compare the numbers 2,37,46,859 and 2,37,56,849. Which number is greater, and write both numbers in words.

Answer:
2,37,56,849 is greater than 2,37,46,859 because the ten thousand place digit in the second number is 5, while in the first number it is 4.
In words:

• 2,37,46,859: Two crore, thirty-seven lakh, forty-six thousand, eight hundred fifty-nine.
• 2,37,56,849: Two crore, thirty-seven lakh, fifty-six thousand, eight hundred forty-nine.

4. Forming a Number:

Create the largest possible number using the digits 5, 3, 7, 6, 9, 1, 4, 2 only once, and write the number in expanded notation.

Answer:
The largest possible number is 97,65,43,210.
Its expanded notation is:
$9 \times 10,00,00,000 + 7 \times 1,00,00,000 + 6 \times 10,00,000 + 5 \times 1,00,000 + 4 \times 10,000 + 3 \times 1,000 + 2 \times 100 + 1 \times 10$.

5. Zero's Impact on Place Value:

If the digit 6 in the number 5,60,43,298 is replaced by a 0, how does this affect the place value of the entire number? What will the new number be?

Answer:
Replacing the 6 in the ten lakhs place with a 0 changes the number from 5,60,43,298 to 5,00,43,298. This decreases the number by 60,00,000 (60 lakhs), since the value contributed by 6 in the ten lakh position is lost.
The new number is 5,00,43,298.

Tip:

When working with large numbers in the Indian system, remember that the placement of commas is crucial for correctly reading and interpreting the number (crores, lakhs, thousands). Practicing expanded notations and comparisons can help with mastering place values.

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