Important Questions: Large Numbers Around Us | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Q1: How many days are there in 200 years (ignoring leap years)? How much less or more is this compared to one lakh? Show your calculations.

Sol: Number of days in a year = 365.
Days in 200 years = 365 × 200 = 73,000.
One lakh = 1,00,000.
Difference = 1,00,000 - 73,000 = 27,000.
The number of days in 200 years is 27,000 less than one lakh.

Q2: Write the following numbers in words using the Indian place value system:
a) 6,08,309
b) 12,50,007

Sol:
a) Six lakh eight thousand three hundred nine.
b) Twelve lakh fifty thousand seven.

Q3: Convert the following number names to numerals in the Indian place value system:
a) Seven lakh forty-two thousand one hundred twenty
b) Three crore five lakh ten thousand four

Sol:
a) 7,42,120
b) 3,05,10,004

Q4: The population of a town was 82,500 in 2015 and is estimated to be 1,12,000 in 2025.
a) How much less than one lakh was the population in 2015?
b) By how much did the population increase from 2015 to 2025?

Sol:
a) One lakh = 1,00,000. Difference = 1,00,000 - 82,500 = 17,500. The population was 17,500 less than one lakh.
b) Increase = 1,12,000 - 82,500 = 29,500. The population increased by 29,500.

Q5: Estimate the sum of 5,27,346 + 3,89,214 to the nearest lakh. Is the exact sum greater or less than 9,00,000? Calculate the exact sum to verify.

Sol:
Round to nearest lakh: 5,27,346 ≈ 5,00,000, 3,89,214 ≈ 4,00,000. 
Estimated sum = 5,00,000 + 4,00,000 = 9,00,000.
Exact sum = 5,27,346 + 3,89,214 = 9,16,560.
Since 9,16,560 > 9,00,000, the exact sum is greater than 9,00,000.

Q6: A building is 36 meters tall, with each floor approximately 3 meters high.
a) How much taller is the Jog Falls waterfall (253 m) than the building?
b) How many floors would the building need to match the height of Jog Falls?

Sol:
a) Difference = 253 - 36 = 217 meters. Jog Falls is 217 meters taller.
b) Height per floor = 3 meters. Number of floors = 253 ÷ 3 ≈ 84.33. Since we can’t have a partial floor, approximately 85 floors are needed.

Q7: If you travel 150 km every day, can you reach Mars (average distance 22,50,00,000 km) in 50 years? Show your calculations and explain.

Sol: Days in 50 years = 365 × 50 = 18,250 days.
Distance traveled = 150 × 18,250 = 27,37,500 km.
Mars distance = 22,50,00,000 km. Since 27,37,500 < 22,50,00,000, you cannot reach Mars in 50 years.

Q8: Calculate 48 × 125 quickly using the fact that 125 = 1000 ÷ 8. Show your steps.

Sol: 48 × 125 = 48 × (1000 ÷ 8) = (48 × 1000) ÷ 8 = 48,000 ÷ 8 = 6,000.

Q9: Verify if the product of two 3-digit numbers can be a 5-digit number. Check the smallest possible product.

Sol: Smallest 3-digit numbers: 100 × 100 = 10,000 (5 digits).
Since the smallest product is 5 digits, the product of two 3-digit numbers can be a 5-digit number.

Q10: How many zeros are in ten thousand lakh? Show your calculation.

Sol: Ten thousand lakh = 10,000 × 1,00,000 = 10,00,00,00,000 .

Q11: Write the number 15,07,82,346 in words using both Indian and American place value systems.

Sol:
Indian: Fifteen crore seven lakh eighty-two thousand three hundred forty-six.
American: One hundred fifty million seven hundred eighty-two thousand three hundred forty-six.

Q12: Using digits 0–9 exactly once (first digit cannot be 0), find:
a) The largest 10-digit multiple of 2.
b) The smallest 10-digit multiple of 5.

Sol:
a) Since a number divisible by 2 must end in an even digit, take the digits in descending order and end with 0 (even):
9876543210
b) A multiple of 5 must end in 0 or 5. To make it as small as possible with first digit ≠ 0, choose last digit 5 (so we can place 0 early). Start with 1, then 0, then remaining digits in ascending order, keeping 5 at the end:
1023467895