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CHAPTER 1 — LARGE NUMBERS AROUND US
Class VII Mathematics — Practice Paper Set 3
Preeti Kushwah Classes
General Instructions:
1. All questions are compulsory.
2. Section A: 6 questions of 1 mark each (6 marks).
3. Section B: 5 questions of 2 marks each (10 marks).
4. Section C: 4 questions of 3 marks each (12 marks).
5. Section D: 2 questions of 4 marks each (8 marks).
6. Bonus: 1 question of 4 marks (optional).
7. Show all working clearly.
1. All questions are compulsory.
2. Section A: 6 questions of 1 mark each (6 marks).
3. Section B: 5 questions of 2 marks each (10 marks).
4. Section C: 4 questions of 3 marks each (12 marks).
5. Section D: 2 questions of 4 marks each (8 marks).
6. Bonus: 1 question of 4 marks (optional).
7. Show all working clearly.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Write the numeral for: Ninety crore eight lakh sixty thousand twelve
Q2.1
How many ten-thousands are there in 1 crore?
Q3.1
The face value of 8 in the number 3,78,45,902 is ___ and its place value is ___.
Q4.1
Which is greater: 99,99,999 or 1,00,00,000? By how much?
Q5.1
Express 456 × 104 in standard form.
Q6.1
Round 3,45,67,891 to the nearest crore.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Write the following in both Indian and International number systems with correct comma placement:
(a) 270546083 (b) 509008400
(a) 270546083 (b) 509008400
Q8.2
Find the successor and predecessor of:
(a) 99,99,999 (b) 10,00,00,000
(a) 99,99,999 (b) 10,00,00,000
Q9.2
Calculate using multiplication shortcuts:
(a) 568 × 999 (b) 784 × 101
(a) 568 × 999 (b) 784 × 101
Q10.2
A builder constructs a building with 18 floors. Each floor is 3.5 metres high. The Statue of Unity is 182 metres tall. How many such buildings placed on top of each other equal the height of the Statue of Unity?
Q11.2
If 1 million = 10 lakh, find the value in lakhs:
(a) 45 million (b) 3.7 million
(a) 45 million (b) 3.7 million
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
In a city election, five candidates got the following votes:
(a) Who won the election? By how many votes did they win over the runner-up?
(b) Find the total votes polled.
(c) Round the winner’s votes to the nearest ten thousand.
| Candidate | Votes |
|---|---|
| A | 3,48,729 |
| B | 5,12,045 |
| C | 2,97,816 |
| D | 4,63,580 |
| E | 1,85,230 |
(b) Find the total votes polled.
(c) Round the winner’s votes to the nearest ten thousand.
Q13.3
A printing press prints 8,500 copies of a newspaper daily. Each copy has 24 pages.
(a) How many total pages are printed in a day?
(b) How many pages in a year (365 days)?
(c) If each page weighs 5 grams, find the total weight of paper used in a year. Express in tonnes. (1 tonne = 10,00,000 grams)
(a) How many total pages are printed in a day?
(b) How many pages in a year (365 days)?
(c) If each page weighs 5 grams, find the total weight of paper used in a year. Express in tonnes. (1 tonne = 10,00,000 grams)
Q14.3
Estimate each product by rounding to the nearest suitable place, then find the actual product:
(a) 673 × 4,891
(b) 8,025 × 396
Compare the estimated and actual products. Which estimate was more accurate?
(a) 673 × 4,891
(b) 8,025 × 396
Compare the estimated and actual products. Which estimate was more accurate?
Q15.3
Form the largest and smallest 8-digit numbers using the digits 3, 0, 5, 2, 8, 1, 6, 9 (each digit used exactly once).
(a) Write both numbers in words (Indian system).
(b) Find their difference.
(c) What is the sum of the place values of 5 in both numbers?
(a) Write both numbers in words (Indian system).
(b) Find their difference.
(c) What is the sum of the place values of 5 in both numbers?
Section D — (4 Marks Each) [2 × 4 = 8]
Q16.4
The distance from Delhi to various cities (by road) is:
Delhi to Mumbai: 1,400 km, Delhi to Chennai: 2,180 km, Delhi to Kolkata: 1,530 km.
A truck travels 350 km per day.
(a) How many days to travel from Delhi to Chennai and back?
(b) In a year (300 working days), how many total km does the truck cover?
(c) Express the yearly distance in words (Indian system).
(d) If diesel costs ₹95 per litre and the truck gives 5 km per litre, find the total fuel cost for the year.
Delhi to Mumbai: 1,400 km, Delhi to Chennai: 2,180 km, Delhi to Kolkata: 1,530 km.
A truck travels 350 km per day.
(a) How many days to travel from Delhi to Chennai and back?
(b) In a year (300 working days), how many total km does the truck cover?
(c) Express the yearly distance in words (Indian system).
(d) If diesel costs ₹95 per litre and the truck gives 5 km per litre, find the total fuel cost for the year.
Q17.4
A school has 2,400 students. Each student is asked to donate ₹15 per month for a tree plantation drive.
(a) What is the total amount collected in one month?
(b) What is the total amount collected in the academic year (10 months)?
(c) If one tree costs ₹450 to plant and maintain for a year, how many trees can be planted?
(d) Each tree absorbs approximately 22 kg of CO2 per year. How many tonnes of CO2 will these trees absorb? (1 tonne = 1,000 kg)
(a) What is the total amount collected in one month?
(b) What is the total amount collected in the academic year (10 months)?
(c) If one tree costs ₹450 to plant and maintain for a year, how many trees can be planted?
(d) Each tree absorbs approximately 22 kg of CO2 per year. How many tonnes of CO2 will these trees absorb? (1 tonne = 1,000 kg)
Bonus Question (Optional) [4 Marks]
Q18.4
★ Without actually multiplying, determine the number of digits in each product. Then verify:
(a) 999 × 99 (b) 1001 × 101 (c) 50000 × 200 (d) 12345 × 6789
State the rule you used and verify any two with actual multiplication.
(a) 999 × 99 (b) 1001 × 101 (c) 50000 × 200 (d) 12345 × 6789
State the rule you used and verify any two with actual multiplication.
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Answer Key & Detailed Solutions
Q1. [1 Mark]
Ninety crore eight lakh sixty thousand twelve
= 90,00,00,000 + 8,00,000 + 60,000 + 12
= 90,08,60,012
= 90,00,00,000 + 8,00,000 + 60,000 + 12
= 90,08,60,012
Q2. [1 Mark]
1 crore = 1,00,00,000
1 ten-thousand = 10,000
1,00,00,000 ÷ 10,000 = 1,000 ten-thousands
1 ten-thousand = 10,000
1,00,00,000 ÷ 10,000 = 1,000 ten-thousands
Q3. [1 Mark]
3,78,45,902
Positions: 3(Cr) 7(TL) 8(L) 4(TTh) 5(Th) 9(H) 0(T) 2(O)
The digit 8 is in the lakhs place.
Face value of 8 = 8
Place value of 8 = 8,00,000 (Eight lakh)
Positions: 3(Cr) 7(TL) 8(L) 4(TTh) 5(Th) 9(H) 0(T) 2(O)
The digit 8 is in the lakhs place.
Face value of 8 = 8
Place value of 8 = 8,00,000 (Eight lakh)
Q4. [1 Mark]
99,99,999 is a 7-digit number.
1,00,00,000 is an 8-digit number.
1,00,00,000 is greater.
Difference = 1,00,00,000 − 99,99,999 = 1
1,00,00,000 is an 8-digit number.
1,00,00,000 is greater.
Difference = 1,00,00,000 − 99,99,999 = 1
Q5. [1 Mark]
456 × 104 = 456 × 10,000 = 45,60,000
(Add 4 zeros to 456)
(Add 4 zeros to 456)
Q6. [1 Mark]
3,45,67,891
Crores digit: 3. Ten-lakhs digit: 4. Since 4 < 5, round down.
Answer: 3,00,00,000 (Three crore)
Crores digit: 3. Ten-lakhs digit: 4. Since 4 < 5, round down.
Answer: 3,00,00,000 (Three crore)
Q7. [2 Marks]
(a) 270546083 [1 mark]
Indian: 27,05,46,083 (Twenty-seven crore five lakh forty-six thousand eighty-three)
International: 270,546,083 (Two hundred seventy million five hundred forty-six thousand eighty-three)
(b) 509008400 [1 mark]
Indian: 50,90,08,400 (Fifty crore ninety lakh eight thousand four hundred)
International: 509,008,400 (Five hundred nine million eight thousand four hundred)
Indian: 27,05,46,083 (Twenty-seven crore five lakh forty-six thousand eighty-three)
International: 270,546,083 (Two hundred seventy million five hundred forty-six thousand eighty-three)
(b) 509008400 [1 mark]
Indian: 50,90,08,400 (Fifty crore ninety lakh eight thousand four hundred)
International: 509,008,400 (Five hundred nine million eight thousand four hundred)
Q8. [2 Marks]
(a) 99,99,999: [1 mark]
Successor = 99,99,999 + 1 = 1,00,00,000
Predecessor = 99,99,999 − 1 = 99,99,998
(b) 10,00,00,000: [1 mark]
Successor = 10,00,00,000 + 1 = 10,00,00,001
Predecessor = 10,00,00,000 − 1 = 9,99,99,999
Successor = 99,99,999 + 1 = 1,00,00,000
Predecessor = 99,99,999 − 1 = 99,99,998
(b) 10,00,00,000: [1 mark]
Successor = 10,00,00,000 + 1 = 10,00,00,001
Predecessor = 10,00,00,000 − 1 = 9,99,99,999
Q9. [2 Marks]
(a) 568 × 999 [1 mark]
Trick: 999 = 1000 − 1
568 × 999 = 568 × 1000 − 568 × 1
= 5,68,000 − 568 = 5,67,432
(b) 784 × 101 [1 mark]
Trick: 101 = 100 + 1
784 × 101 = 784 × 100 + 784 × 1
= 78,400 + 784 = 79,184
Trick: 999 = 1000 − 1
568 × 999 = 568 × 1000 − 568 × 1
= 5,68,000 − 568 = 5,67,432
(b) 784 × 101 [1 mark]
Trick: 101 = 100 + 1
784 × 101 = 784 × 100 + 784 × 1
= 78,400 + 784 = 79,184
Q10. [2 Marks]
Height of one building = 18 × 3.5 = 63 metres [1 mark]
Height of Statue of Unity = 182 metres
Number of buildings = 182 ÷ 63 = 2.889... ≈ 3 buildings [1 mark]
(Need 3 buildings since 2 buildings = 126m, which is less than 182m)
Height of Statue of Unity = 182 metres
Number of buildings = 182 ÷ 63 = 2.889... ≈ 3 buildings [1 mark]
(Need 3 buildings since 2 buildings = 126m, which is less than 182m)
Q11. [2 Marks]
(a) 45 million = 45 × 10 lakh = 450 lakh (= 4,50,00,000) [1 mark]
(b) 3.7 million = 3.7 × 10 lakh = 37 lakh (= 37,00,000) [1 mark]
(b) 3.7 million = 3.7 × 10 lakh = 37 lakh (= 37,00,000) [1 mark]
Q12. [3 Marks]
(a) Winner: [1 mark]
B got most votes (5,12,045). Runner-up is D (4,63,580).
Winning margin = 5,12,045 − 4,63,580 = 48,465 votes
(b) Total votes: [1 mark]
3,48,729 + 5,12,045 + 2,97,816 + 4,63,580 + 1,85,230
= 18,07,400 (Eighteen lakh seven thousand four hundred)
(c) Winner rounded to nearest ten thousand: [1 mark]
5,12,045 → thousands digit is 2, which is < 5. Round down.
Answer: 5,10,000
B got most votes (5,12,045). Runner-up is D (4,63,580).
Winning margin = 5,12,045 − 4,63,580 = 48,465 votes
(b) Total votes: [1 mark]
3,48,729 + 5,12,045 + 2,97,816 + 4,63,580 + 1,85,230
= 18,07,400 (Eighteen lakh seven thousand four hundred)
(c) Winner rounded to nearest ten thousand: [1 mark]
5,12,045 → thousands digit is 2, which is < 5. Round down.
Answer: 5,10,000
Q13. [3 Marks]
(a) Pages per day: [1 mark]
8,500 × 24 = 2,04,000 pages
(b) Pages per year: [1 mark]
2,04,000 × 365 = 7,44,60,000 pages
= Seven crore forty-four lakh sixty thousand
(c) Weight in tonnes: [1 mark]
Total weight = 7,44,60,000 × 5 = 37,23,00,000 grams
In tonnes = 37,23,00,000 ÷ 10,00,000 = 3,723 tonnes
= Three thousand seven hundred twenty-three tonnes
8,500 × 24 = 2,04,000 pages
(b) Pages per year: [1 mark]
2,04,000 × 365 = 7,44,60,000 pages
= Seven crore forty-four lakh sixty thousand
(c) Weight in tonnes: [1 mark]
Total weight = 7,44,60,000 × 5 = 37,23,00,000 grams
In tonnes = 37,23,00,000 ÷ 10,00,000 = 3,723 tonnes
= Three thousand seven hundred twenty-three tonnes
Q14. [3 Marks]
(a) 673 × 4,891: [1½ marks]
Estimation: 700 × 5,000 = 35,00,000
Actual: 673 × 4,891 = 32,91,643
Error = 35,00,000 − 32,91,643 = 2,08,357 (6.3% error)
(b) 8,025 × 396: [1½ marks]
Estimation: 8,000 × 400 = 32,00,000
Actual: 8,025 × 396 = 31,77,900
Error = 32,00,000 − 31,77,900 = 22,100 (0.7% error)
Answer: (b) was more accurate because the rounding errors cancelled each other (8,025 rounded down, 396 rounded up).
Estimation: 700 × 5,000 = 35,00,000
Actual: 673 × 4,891 = 32,91,643
Error = 35,00,000 − 32,91,643 = 2,08,357 (6.3% error)
(b) 8,025 × 396: [1½ marks]
Estimation: 8,000 × 400 = 32,00,000
Actual: 8,025 × 396 = 31,77,900
Error = 32,00,000 − 31,77,900 = 22,100 (0.7% error)
Answer: (b) was more accurate because the rounding errors cancelled each other (8,025 rounded down, 396 rounded up).
Q15. [3 Marks]
Digits: 0, 1, 2, 3, 5, 6, 8, 9
Largest 8-digit: 9,86,53,210 [½ mark]
= Nine crore eighty-six lakh fifty-three thousand two hundred ten
Smallest 8-digit: 1,02,35,689 [½ mark]
= One crore two lakh thirty-five thousand six hundred eighty-nine
(b) Difference: [1 mark]
9,86,53,210 − 1,02,35,689 = 8,84,17,521
(c) Place value of 5: [1 mark]
In 9,86,53,210: 5 is in ten-thousands place = 50,000
In 1,02,35,689: 5 is in thousands place = 5,000
Sum = 50,000 + 5,000 = 55,000
Largest 8-digit: 9,86,53,210 [½ mark]
= Nine crore eighty-six lakh fifty-three thousand two hundred ten
Smallest 8-digit: 1,02,35,689 [½ mark]
= One crore two lakh thirty-five thousand six hundred eighty-nine
(b) Difference: [1 mark]
9,86,53,210 − 1,02,35,689 = 8,84,17,521
(c) Place value of 5: [1 mark]
In 9,86,53,210: 5 is in ten-thousands place = 50,000
In 1,02,35,689: 5 is in thousands place = 5,000
Sum = 50,000 + 5,000 = 55,000
Q16. [4 Marks]
(a) Days for Delhi-Chennai round trip: [1 mark]
Round trip = 2,180 × 2 = 4,360 km
Days = 4,360 ÷ 350 = 12.46 ≈ 13 days
(b) Yearly distance: [1 mark]
350 × 300 = 1,05,000 km
(c) In words: [½ mark]
One lakh five thousand kilometres
(d) Fuel cost: [1½ marks]
Litres needed = 1,05,000 ÷ 5 = 21,000 litres
Cost = 21,000 × 95 = ₹19,95,000
= Nineteen lakh ninety-five thousand rupees
Round trip = 2,180 × 2 = 4,360 km
Days = 4,360 ÷ 350 = 12.46 ≈ 13 days
(b) Yearly distance: [1 mark]
350 × 300 = 1,05,000 km
(c) In words: [½ mark]
One lakh five thousand kilometres
(d) Fuel cost: [1½ marks]
Litres needed = 1,05,000 ÷ 5 = 21,000 litres
Cost = 21,000 × 95 = ₹19,95,000
= Nineteen lakh ninety-five thousand rupees
Q17. [4 Marks]
(a) Monthly collection: [1 mark]
2,400 × 15 = ₹36,000
(b) Annual collection (10 months): [1 mark]
36,000 × 10 = ₹3,60,000
(c) Number of trees: [1 mark]
3,60,000 ÷ 450 = 800 trees
(d) CO2 absorbed: [1 mark]
800 × 22 = 17,600 kg
In tonnes = 17,600 ÷ 1,000 = 17.6 tonnes of CO2
2,400 × 15 = ₹36,000
(b) Annual collection (10 months): [1 mark]
36,000 × 10 = ₹3,60,000
(c) Number of trees: [1 mark]
3,60,000 ÷ 450 = 800 trees
(d) CO2 absorbed: [1 mark]
800 × 22 = 17,600 kg
In tonnes = 17,600 ÷ 1,000 = 17.6 tonnes of CO2
Q18. Bonus [4 Marks]
Rule: If a number has m digits and another has n digits, their product has at least (m + n − 1) and at most (m + n) digits. [1 mark for rule]
(a) 999 × 99: m=3, n=2 → 4 to 5 digits [½ mark]
Actual: 999 × 99 = 98,901 → 5 digits ✅
(b) 1001 × 101: m=4, n=3 → 6 to 7 digits [½ mark]
Actual: 1001 × 101 = 1,01,101 → 6 digits ✅
(c) 50000 × 200: m=5, n=3 → 7 to 8 digits [½ mark]
Actual: 50,000 × 200 = 1,00,00,000 → 8 digits ✅
(d) 12345 × 6789: m=5, n=4 → 8 to 9 digits [½ mark]
Actual: 12,345 × 6,789 = 8,38,10,205 → 8 digits ✅
(Any two verifications with full computation earn the marks)
(a) 999 × 99: m=3, n=2 → 4 to 5 digits [½ mark]
Actual: 999 × 99 = 98,901 → 5 digits ✅
(b) 1001 × 101: m=4, n=3 → 6 to 7 digits [½ mark]
Actual: 1001 × 101 = 1,01,101 → 6 digits ✅
(c) 50000 × 200: m=5, n=3 → 7 to 8 digits [½ mark]
Actual: 50,000 × 200 = 1,00,00,000 → 8 digits ✅
(d) 12345 × 6789: m=5, n=4 → 8 to 9 digits [½ mark]
Actual: 12,345 × 6,789 = 8,38,10,205 → 8 digits ✅
(Any two verifications with full computation earn the marks)