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CHAPTER 1 — LARGE NUMBERS AROUND US
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test
General Instructions:
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Write the numeral for: Thirty-two lakh seven thousand ninety
Q2.1
How many lakhs make one crore?
Q3.1
Round 48,73,562 to the nearest lakh.
Q4.1
Place the correct symbol (<, > or =): 50 lakhs ___ 5 million
Q5.1
A calculator has only a +100 button. How many presses to show 7,200 on the screen?
Q6.1
The product of a 3-digit number and a 2-digit number will have at least ___ digits and at most ___ digits.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Write the following number in both Indian and International systems. Also write in words in both systems.
59,40,38,072
59,40,38,072
Q8.2
A calculator has buttons: +1, +10, +100, +1000. What is the minimum number of button clicks to reach 47,253? Explain your reasoning.
Q9.2
Find all 4 nearest neighbours of the number 6,83,47,215:
(a) Nearest Thousand (b) Nearest Ten Thousand (c) Nearest Lakh (d) Nearest Crore
(a) Nearest Thousand (b) Nearest Ten Thousand (c) Nearest Lakh (d) Nearest Crore
Q10.2
Calculate using a shortcut (show the trick):
(a) 248 × 25 (b) 64 × 125
(a) 248 × 25 (b) 64 × 125
Q11.2
India has approximately 1,00,000 varieties of rice. If a person tastes 4 varieties every day, how many years will it take to taste all of them? (Take 1 year = 365 days)
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Study the table and answer the questions below:
(a) Arrange the cities in descending order of population.
(b) What is the difference between the populations of Bengaluru and Pune?
(c) Round Hyderabad’s population to the nearest ten lakh.
| City | Population (2011) |
|---|---|
| Bengaluru | 84,25,970 |
| Hyderabad | 68,09,970 |
| Pune | 31,15,431 |
| Surat | 44,67,797 |
(b) What is the difference between the populations of Bengaluru and Pune?
(c) Round Hyderabad’s population to the nearest ten lakh.
Q13.3
A school raises funds for flood relief. They collect ₹275 from each of 1,850 students. The principal adds ₹48,500 from the school fund.
(a) What is the total amount collected?
(b) Express the total in words (Indian system).
(c) If the target was ₹6,00,000, how much more is needed?
(a) What is the total amount collected?
(b) Express the total in words (Indian system).
(c) If the target was ₹6,00,000, how much more is needed?
Q14.3
Estimate the product 489 × 7,210 by rounding each number. Then find the exact product. How close was your estimate?
Q15.3
Using the digits 0, 3, 5, 7, 8 (each used exactly once):
(a) Write the largest 5-digit number.
(b) Write the smallest 5-digit number.
(c) Find the difference between them.
(a) Write the largest 5-digit number.
(b) Write the smallest 5-digit number.
(c) Find the difference between them.
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
(a) A factory produces 12,500 bottles per day. It operates 6 days a week.
(i) How many bottles in a week?
(ii) How many bottles in a year (52 weeks)?
(iii) Express the yearly production in words (Indian system).
(iv) If each bottle weighs 250 grams, what is the total weight in tonnes? (1 tonne = 10,00,000 g)
(b) The factory wants to reach a target of 50 lakh bottles per year. How many extra bottles must they produce daily (over 6 days/week, 52 weeks)?
(i) How many bottles in a week?
(ii) How many bottles in a year (52 weeks)?
(iii) Express the yearly production in words (Indian system).
(iv) If each bottle weighs 250 grams, what is the total weight in tonnes? (1 tonne = 10,00,000 g)
(b) The factory wants to reach a target of 50 lakh bottles per year. How many extra bottles must they produce daily (over 6 days/week, 52 weeks)?
Q17.5
(a) A satellite orbits the Earth at 28,000 km/hour.
(i) How many km does it travel in one day?
(ii) How many days to cover a distance equal to Earth–Sun (15,00,00,000 km)?
(iii) Round your answer to the nearest hundred days.
(b) The Moon is 3,84,400 km from Earth. If a spacecraft travels at 1,200 km/hour:
(i) How many hours to reach the Moon?
(ii) How many complete days is that? Express the remaining hours too.
(i) How many km does it travel in one day?
(ii) How many days to cover a distance equal to Earth–Sun (15,00,00,000 km)?
(iii) Round your answer to the nearest hundred days.
(b) The Moon is 3,84,400 km from Earth. If a spacecraft travels at 1,200 km/hour:
(i) How many hours to reach the Moon?
(ii) How many complete days is that? Express the remaining hours too.
Bonus Question (Optional) [2 Marks]
Q18.2
★ A number when rounded to the nearest lakh gives 35,00,000 and when rounded to the nearest ten thousand gives 34,90,000. Find the range of possible values of the number.
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Answer Key & Detailed Solutions
Q1. [1 Mark]
Thirty-two lakh seven thousand ninety
= 32,00,000 + 7,000 + 90
= 32,07,090
= 32,00,000 + 7,000 + 90
= 32,07,090
Q2. [1 Mark]
1 Crore = 1,00,00,000
1 Lakh = 1,00,000
1,00,00,000 ÷ 1,00,000 = 100 lakhs make one crore.
1 Lakh = 1,00,000
1,00,00,000 ÷ 1,00,000 = 100 lakhs make one crore.
Q3. [1 Mark]
48,73,562 → Look at the ten-thousands digit: 7
Since 7 ≥ 5, round up the lakh digit (8 becomes 9).
Wait — let’s be careful: 48,73,562. The lakhs digit is 8. The digit after lakhs place (ten-thousands) is 7.
Since 7 ≥ 5, round up: 48 lakhs becomes 49 lakhs.
Answer: 49,00,000
Since 7 ≥ 5, round up the lakh digit (8 becomes 9).
Wait — let’s be careful: 48,73,562. The lakhs digit is 8. The digit after lakhs place (ten-thousands) is 7.
Since 7 ≥ 5, round up: 48 lakhs becomes 49 lakhs.
Answer: 49,00,000
Q4. [1 Mark]
50 lakhs = 50,00,000
5 million = 50,00,000 (since 1 million = 10 lakh)
50,00,000 = 50,00,000
Answer: 50 lakhs = 5 million
5 million = 50,00,000 (since 1 million = 10 lakh)
50,00,000 = 50,00,000
Answer: 50 lakhs = 5 million
Q5. [1 Mark]
7,200 ÷ 100 = 72 presses
Q6. [1 Mark]
Smallest: 100 × 10 = 1,000 (4 digits)
Largest: 999 × 99 = 98,901 (5 digits)
Answer: at least 4 digits and at most 5 digits.
Rule: m + n − 1 to m + n digits → 3 + 2 − 1 = 4 to 3 + 2 = 5.
Largest: 999 × 99 = 98,901 (5 digits)
Answer: at least 4 digits and at most 5 digits.
Rule: m + n − 1 to m + n digits → 3 + 2 − 1 = 4 to 3 + 2 = 5.
Q7. [2 Marks]
Indian system: 59,40,38,072
In words: Fifty-nine crore forty lakh thirty-eight thousand seventy-two
International system: 594,038,072
In words: Five hundred ninety-four million thirty-eight thousand seventy-two
(1 mark for correct comma placement + 1 mark for correct words in both systems)
In words: Fifty-nine crore forty lakh thirty-eight thousand seventy-two
International system: 594,038,072
In words: Five hundred ninety-four million thirty-eight thousand seventy-two
(1 mark for correct comma placement + 1 mark for correct words in both systems)
Q8. [2 Marks]
47,253 = 4 × 10,000 + 7 × 1,000 + 2 × 100 + 5 × 10 + 3 × 1
Optimal strategy: use the +1000 button for thousands and above.
+1000 pressed: 4 × 10 + 7 = 47 times (to make 47,000) [1 mark]
+100 pressed: 2 times (to add 200)
+10 pressed: 5 times (to add 50)
+1 pressed: 3 times (to add 3)
Total = 47 + 2 + 5 + 3 = 57 clicks [1 mark]
Optimal strategy: use the +1000 button for thousands and above.
+1000 pressed: 4 × 10 + 7 = 47 times (to make 47,000) [1 mark]
+100 pressed: 2 times (to add 200)
+10 pressed: 5 times (to add 50)
+1 pressed: 3 times (to add 3)
Total = 47 + 2 + 5 + 3 = 57 clicks [1 mark]
Q9. [2 Marks]
Number: 6,83,47,215
(a) Nearest Thousand: Look at hundreds digit (2). Since 2 < 5, round down.
→ 6,83,47,000 [½ mark]
(b) Nearest Ten Thousand: Look at thousands digit (7). Since 7 ≥ 5, round up.
→ 6,83,50,000 [½ mark]
(c) Nearest Lakh: Look at ten-thousands digit (4). Since 4 < 5, round down.
→ 6,83,00,000 [½ mark]
(d) Nearest Crore: Look at ten-lakhs digit (8). Since 8 ≥ 5, round up.
→ 7,00,00,000 [½ mark]
(a) Nearest Thousand: Look at hundreds digit (2). Since 2 < 5, round down.
→ 6,83,47,000 [½ mark]
(b) Nearest Ten Thousand: Look at thousands digit (7). Since 7 ≥ 5, round up.
→ 6,83,50,000 [½ mark]
(c) Nearest Lakh: Look at ten-thousands digit (4). Since 4 < 5, round down.
→ 6,83,00,000 [½ mark]
(d) Nearest Crore: Look at ten-lakhs digit (8). Since 8 ≥ 5, round up.
→ 7,00,00,000 [½ mark]
Q10. [2 Marks]
(a) 248 × 25 [1 mark]
Trick: 25 = 100 ÷ 4
248 × 100 = 24,800
24,800 ÷ 4 = 6,200
(b) 64 × 125 [1 mark]
Trick: 125 = 1000 ÷ 8
64 × 1000 = 64,000
64,000 ÷ 8 = 8,000
Alternative for (b): 64 × 125 = 8 × 8 × 125 = 8 × 1000 = 8,000
Trick: 25 = 100 ÷ 4
248 × 100 = 24,800
24,800 ÷ 4 = 6,200
(b) 64 × 125 [1 mark]
Trick: 125 = 1000 ÷ 8
64 × 1000 = 64,000
64,000 ÷ 8 = 8,000
Alternative for (b): 64 × 125 = 8 × 8 × 125 = 8 × 1000 = 8,000
Q11. [2 Marks]
Varieties per day = 4
Varieties per year = 4 × 365 = 1,460 [1 mark]
Years needed = 1,00,000 ÷ 1,460 ≈ 68.49 years [1 mark]
Answer: It will take approximately 69 years (rounding up since you can’t taste a fraction of a year’s worth).
Varieties per year = 4 × 365 = 1,460 [1 mark]
Years needed = 1,00,000 ÷ 1,460 ≈ 68.49 years [1 mark]
Answer: It will take approximately 69 years (rounding up since you can’t taste a fraction of a year’s worth).
Q12. [3 Marks]
(a) Descending order of population: [1 mark]
Bengaluru (84,25,970) > Hyderabad (68,09,970) > Surat (44,67,797) > Pune (31,15,431)
(b) Difference between Bengaluru and Pune: [1 mark]
84,25,970 − 31,15,431 = 53,10,539
= Fifty-three lakh ten thousand five hundred thirty-nine
(c) Hyderabad nearest ten lakh: [1 mark]
68,09,970 → Look at the lakh digit: 8. Since 8 ≥ 5, round up.
Answer: 70,00,000 (Seventy lakh)
Bengaluru (84,25,970) > Hyderabad (68,09,970) > Surat (44,67,797) > Pune (31,15,431)
(b) Difference between Bengaluru and Pune: [1 mark]
84,25,970 − 31,15,431 = 53,10,539
= Fifty-three lakh ten thousand five hundred thirty-nine
(c) Hyderabad nearest ten lakh: [1 mark]
68,09,970 → Look at the lakh digit: 8. Since 8 ≥ 5, round up.
Answer: 70,00,000 (Seventy lakh)
Q13. [3 Marks]
(a) Total collected: [1 mark]
From students: 275 × 1,850
= 275 × 1,000 + 275 × 850
= 2,75,000 + 2,33,750
= 5,08,750
Adding principal’s contribution: 5,08,750 + 48,500 = ₹5,57,250
(b) In words: [1 mark]
Five lakh fifty-seven thousand two hundred fifty rupees
(c) More needed: [1 mark]
6,00,000 − 5,57,250 = ₹42,750 more is needed.
= Forty-two thousand seven hundred fifty rupees.
From students: 275 × 1,850
= 275 × 1,000 + 275 × 850
= 2,75,000 + 2,33,750
= 5,08,750
Adding principal’s contribution: 5,08,750 + 48,500 = ₹5,57,250
(b) In words: [1 mark]
Five lakh fifty-seven thousand two hundred fifty rupees
(c) More needed: [1 mark]
6,00,000 − 5,57,250 = ₹42,750 more is needed.
= Forty-two thousand seven hundred fifty rupees.
Q14. [3 Marks]
Estimation: [1 mark]
489 ≈ 500 (nearest hundred)
7,210 ≈ 7,000 (nearest thousand)
Estimated product: 500 × 7,000 = 35,00,000
Exact product: [1 mark]
489 × 7,210
= 489 × 7,000 + 489 × 210
= 34,23,000 + 1,02,690
= 35,25,690
Comparison: [1 mark]
Difference = 35,25,690 − 35,00,000 = 25,690
Error percentage = 25,690 / 35,25,690 × 100 ≈ 0.73%
The estimate was very close — less than 1% error!
489 ≈ 500 (nearest hundred)
7,210 ≈ 7,000 (nearest thousand)
Estimated product: 500 × 7,000 = 35,00,000
Exact product: [1 mark]
489 × 7,210
= 489 × 7,000 + 489 × 210
= 34,23,000 + 1,02,690
= 35,25,690
Comparison: [1 mark]
Difference = 35,25,690 − 35,00,000 = 25,690
Error percentage = 25,690 / 35,25,690 × 100 ≈ 0.73%
The estimate was very close — less than 1% error!
Q15. [3 Marks]
Available digits: 0, 3, 5, 7, 8
(a) Largest 5-digit number: [1 mark]
Arrange in descending order: 87,530
(b) Smallest 5-digit number: [1 mark]
First digit cannot be 0, so use 3 (smallest non-zero).
Then arrange remaining (0, 5, 7, 8) in ascending: 0, 5, 7, 8
Answer: 30,578
(c) Difference: [1 mark]
87,530 − 30,578 = 56,952
(a) Largest 5-digit number: [1 mark]
Arrange in descending order: 87,530
(b) Smallest 5-digit number: [1 mark]
First digit cannot be 0, so use 3 (smallest non-zero).
Then arrange remaining (0, 5, 7, 8) in ascending: 0, 5, 7, 8
Answer: 30,578
(c) Difference: [1 mark]
87,530 − 30,578 = 56,952
Q16. [5 Marks]
(a)(i) Bottles per week: [1 mark]
12,500 × 6 = 75,000 bottles
(a)(ii) Bottles per year: [1 mark]
75,000 × 52 = 39,00,000 bottles
(a)(iii) In words: [½ mark]
Thirty-nine lakh bottles
(a)(iv) Total weight: [1 mark]
Weight = 39,00,000 × 250 = 97,50,00,000 grams
In tonnes = 97,50,00,000 ÷ 10,00,000 = 975 tonnes
(b) Extra bottles needed daily: [1½ marks]
Target: 50,00,000 bottles/year
Current: 39,00,000 bottles/year
Shortfall: 50,00,000 − 39,00,000 = 11,00,000 bottles/year
Working days/year: 6 × 52 = 312 days
Extra per day: 11,00,000 ÷ 312 ≈ 3,526 extra bottles/day
New daily production ≈ 12,500 + 3,526 = 16,026 bottles/day
12,500 × 6 = 75,000 bottles
(a)(ii) Bottles per year: [1 mark]
75,000 × 52 = 39,00,000 bottles
(a)(iii) In words: [½ mark]
Thirty-nine lakh bottles
(a)(iv) Total weight: [1 mark]
Weight = 39,00,000 × 250 = 97,50,00,000 grams
In tonnes = 97,50,00,000 ÷ 10,00,000 = 975 tonnes
(b) Extra bottles needed daily: [1½ marks]
Target: 50,00,000 bottles/year
Current: 39,00,000 bottles/year
Shortfall: 50,00,000 − 39,00,000 = 11,00,000 bottles/year
Working days/year: 6 × 52 = 312 days
Extra per day: 11,00,000 ÷ 312 ≈ 3,526 extra bottles/day
New daily production ≈ 12,500 + 3,526 = 16,026 bottles/day
Q17. [5 Marks]
(a)(i) Distance in one day: [1 mark]
28,000 × 24 = 6,72,000 km/day
(a)(ii) Days to reach the Sun: [1 mark]
15,00,00,000 ÷ 6,72,000 ≈ 223.2 days
(a)(iii) Rounded to nearest hundred: [½ mark]
223.2 → 200 days (nearest hundred)
(b)(i) Hours to reach the Moon: [1½ marks]
3,84,400 ÷ 1,200 = 320.33 hours
(b)(ii) Complete days + remaining hours: [1 mark]
320.33 ÷ 24 = 13 days remainder 8.33 hours
Answer: 13 complete days and approximately 8 hours
28,000 × 24 = 6,72,000 km/day
(a)(ii) Days to reach the Sun: [1 mark]
15,00,00,000 ÷ 6,72,000 ≈ 223.2 days
(a)(iii) Rounded to nearest hundred: [½ mark]
223.2 → 200 days (nearest hundred)
(b)(i) Hours to reach the Moon: [1½ marks]
3,84,400 ÷ 1,200 = 320.33 hours
(b)(ii) Complete days + remaining hours: [1 mark]
320.33 ÷ 24 = 13 days remainder 8.33 hours
Answer: 13 complete days and approximately 8 hours
Q18. Bonus [2 Marks]
Condition 1: Rounded to nearest lakh = 35,00,000 [1 mark]
This means: 34,50,000 ≤ N ≤ 35,49,999
Condition 2: Rounded to nearest ten thousand = 34,90,000 [1 mark]
This means: 34,85,000 ≤ N ≤ 34,94,999
Both conditions together:
The number must satisfy BOTH ranges.
Intersection: max(34,50,000, 34,85,000) ≤ N ≤ min(35,49,999, 34,94,999)
→ 34,85,000 ≤ N ≤ 34,94,999
The number lies between 34,85,000 and 34,94,999 (a range of 10,000 values).
This means: 34,50,000 ≤ N ≤ 35,49,999
Condition 2: Rounded to nearest ten thousand = 34,90,000 [1 mark]
This means: 34,85,000 ≤ N ≤ 34,94,999
Both conditions together:
The number must satisfy BOTH ranges.
Intersection: max(34,50,000, 34,85,000) ≤ N ≤ min(35,49,999, 34,94,999)
→ 34,85,000 ≤ N ≤ 34,94,999
The number lies between 34,85,000 and 34,94,999 (a range of 10,000 values).