Class 7 Maths Ch 1: Large Numbers Around Us – learn lakhs, crores, place value, estimation and factorisation through stories and puzzles, with notes, solved sums, extra questions and quiz for CBSE Exam
Complete Chapter 1 guide: understanding one lakh and other large numbers using real‑life stories (rice varieties, populations, heights, waterfalls, travel distances), Indian and international place value systems, reading and writing large numbers in words and figures, comparing and estimating big quantities, simple factorisation and regrouping to make multiplication easier, plus solved examples, practice questions, word problems and puzzles (Land of Tens calculators, toothpick digits) for CBSE Class 7 Math
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Large Numbers Around Us
Class 7 Mathematics Chapter 1 | Complete NCERT Guide | Place Value, Approximation, Multiplication Patterns 2025
Chapter at a Glance – Large Numbers Around Us
This chapter introduces large numbers like lakhs and crores, place value systems, approximation, and multiplication patterns. Key focus: Understanding scale, reading/writing numbers, and real-life applications.
Main Topics Covered
- What is a lakh? (1,00,000) – Examples with rice varieties, lifetimes.
- Comparing large numbers (heights, populations).
- Indian place value system (thousands, lakhs, crores).
- Land of Tens activities (adding with buttons, place value).
- Crores and beyond (comparison with American system).
- Exact vs approximate values (rounding up/down).
- Nearest neighbours (rounding to thousand/lakh).
- Estimating sums/differences.
- Population data analysis.
- Multiplication shortcuts and patterns.
- Fascinating facts with calculations.
- Thought experiments (e.g., fitting population in buses).
Key Takeaways for Exams
Lakh & Crore
1 lakh = 1,00,000 (5 zeros)
1 crore = 1,00,00,000 (7 zeros)
Indian vs American
Indian: 1,00,000 (lakh)
American: 100,000 (hundred thousand)
Rounding
Round up for more (e.g., sweets), down for less (e.g., cost).
Multiplication
n-digit × m-digit = (n+m-1) or (n+m) digits.
Key Concepts & Formulas – Large Numbers
Important concepts, formulas, place value charts, and tips for quick calculations.
Place Value Charts
| Indian System | |
|---|---|
| 1,00,00,000 | 1 Crore |
| 10,00,000 | 10 Lakh |
| 1,00,000 | 1 Lakh |
| 10,000 | 10 Thousand |
| 1,000 | 1 Thousand |
| American System | |
|---|---|
| 1,000,000,000 | 1 Billion |
| 100,000,000 | 100 Million |
| 10,000,000 | 10 Million |
| 1,000,000 | 1 Million |
| 100,000 | 100 Thousand |
Key Formulas & Tips
- 1 Lakh = 100 × 1 Thousand = 1,00,000
- 1 Crore = 100 × 1 Lakh = 1,00,00,000
- Number of days in y years ≈ 365 × y
- Multiplication by 10/100/1000: Add zeros at end
- Multiplication by 5: ×10 / 2
- Multiplication by 25: ×100 / 4
- Number of digits in product: Min = n+m-1, Max = n+m (for n-digit × m-digit)
Golden Lines for Exams
“In Indian system, commas are placed as 3-2-2 from right; in American, 3-3-3.”
Concept Cards – Quick Explanations
Lakh Concept
1 lakh = 100,000. Example: 1 lakh days = 274 years (1,00,000 ÷ 365 ≈ 274).
Exam Tip: Use for population, lifetime calculations.
Place Value
Indian: Units, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores.
Example: 1,23,45,678 = 1 Crore 23 Lakh 45 Thousand 678.
Rounding
Round up: More than actual (e.g., sweets: 732 → 750).
Round down: Less (e.g., cost: 470 → 450).
Multiplication Patterns
11 × 11 = 121, 111 × 111 = 12321 (palindromic).
n-digit × m-digit: Digits between n+m-1 and n+m.
Estimation
Nearest thousand/lakh: For quick sums/differences.
Example: 4,63,128 + 4,19,682 ≈ 8,80,000 (actual 8,82,810).
NCERT Examples + Solutions
Example 1: Lifetime Rice Varieties
If 1 variety per day, in 100 years: 365 × 100 = 36,500 varieties (less than 1 lakh).
2 per day: 73,000 (still less).
3 per day: 1,09,500 (more than 1 lakh).
Example 2: Building Height Comparison
Somu 1m, floor 4m, building 10 floors = 40m.
Statue of Unity 180m - 40m = 140m taller.
Kunchikal 450m - 40m = 410m taller.
Floors for waterfall: 450 / 4 = 112.5 ≈ 113 floors.
Example 3: Lakh Big or Small
Large: 1 lakh people line = 38km.
Small: Stadium fits 1 lakh, hair 1 lakh on head.
Exercise Wise Solutions (Selected) – All Figure it Out Solved
Figure it Out (Page 3)
1. Chintamani population 2011: 75,000 less than 1 lakh?
1,00,000 - 75,000 = 25,000 less.
2. 2024: 1,06,000 more than 1 lakh?
1,06,000 - 1,00,000 = 6,000 more.
3. Increase from 2011 to 2024?
1,06,000 - 75,000 = 31,000 increase.
Figure it Out (Heights)
Statue vs Building
180 - 40 = 140m taller.
Waterfall vs Building
450 - 40 = 410m taller.
Floors for Waterfall
450 / 4 = 112.5 ≈ 113 floors.
Reading/Writing Numbers (Page 4)
Write in words
(a) Three lakh six hundred
(b) Five lakh four thousand eighty five
(c) Twenty seven lakh thirty thousand
(d) Seventy lakh fifty three thousand one hundred thirty eight
Write numbers
(a) 1,23,456
(b) 4,07,704
(c) 50,05,050
(d) 10,00,235
Land of Tens (Page 5)
1. Thoughtful Thousands (+1000)
(b) 10 times
(c) 53 times
(d) 90 times
(e) 100 times
(g) 100
2. Tedious Tens (+10)
(a) 50 times
(b) 78 times
(c) 100 times
(d) 370 times
(e) 1000 times
(f) 10,000 times
3. Handy Hundreds (+100)
(a) 4 times
(b) 37 times
(c) 100 times
(d) 530 times
(e) 900 times
(f) 976 times
(g) 1000 times
(i) 100
(j) 1000
(k) Yes, numbers not multiples of 100.
Creative Chitti (Page 6)
4. Different way for 5072
(5×1000) + (0×100) + (7×10) + (2×1) = 5072
5. Expressions for numbers
(a) (8×1000) + (3×100) + (0×10) + (0×1)
(b) (4×10000) + (0×1000) + (6×100) + (2×10) + (9×1)
(c) (5×10000) + (6×1000) + (3×100) + (5×10) + (4×1)
(d) (6×10000) + (6×1000) + (6×100) + (6×10) + (6×1)
(e) (3×100000) + (6×10000) + (7×1000) + (8×100) + (1×10) + (3×1)
Systematic Sippy (Page 7)
7. Minimal clicks
(a) 2×10000 + 0×1000 + 8×100 + 0×10 + 0×1
(b) 9×10000 + 2×1000 + 1×100 + 0×10 + 0×1
(c) 1×100000 + 2×10000 + 0×1000 + 5×100 + 0×10 + 0×1
(d) 6×1000000 + 5×100000 + 3×10000 + 0×1000 + 0×100 + 0×10 + 0×1
(e) 7×1000000 + 0×100000 + 2×10000 + 5×1000 + 7×100 + 0×10 + 0×1
Crores (Page 8)
How many zeros in thousand lakh?
1000 × 1,00,000 = 10,00,00,000 (8 zeros).
Figure it Out (Page 9)
1. Read numbers
(a) Indian: Forty lakh fifty thousand six hundred seventy eight; American: Four million fifty thousand six hundred seventy eight.
(b) Indian: Four crore eighty one lakh twenty one thousand six hundred twenty; American: Forty eight million one hundred twenty one thousand six hundred twenty.
(c) Indian: Two crore two lakh twenty thousand two; American: Twenty million two hundred twenty thousand two.
(d) Indian: Twenty four crore sixty eight lakh thirteen thousand five hundred seventy nine; American: Two hundred forty six million eight hundred thirteen thousand five hundred seventy nine.
(e) Indian: Thirty four crore fifty lakh five hundred forty three; American: Three hundred forty five million five hundred forty three.
(f) Indian: One hundred two crore three lakh four thousand fifty; American: One billion twenty million three hundred four thousand fifty.
2. Write numbers
(a) 1,01,01,010
(b) 1,001,001,001
(c) 10,20,30,040
(d) 9,080,700,600
3. Compare
(a) 30,000 < 3,00,000
(b) 5,00,000 < 5,000,000
(c) 8,00,000 < 8,000,000
(d) 640,00,00,000 > 60,000,000,000
Rounding (Page 10)
Situations for rounding
(a) Round up: Ordering food for party (guests 98 → order for 100).
(b) Round down: Budgeting expense (cost 472 → estimate 470).
(c) Either: Approximate distance (120km → 100 or 150).
(d) Exact: Exam marks, bank balance.
Nearest Neighbours (Page 11)
Nearest for 3,87,69,957
Thousand: 3,87,70,000
Ten thousand: 3,87,70,000
Lakh: 3,88,00,000
Ten lakh: 3,90,00,000
Crore: 4,00,00,000
Nearest for 29,05,32,481
Thousand: 29,05,32,000
Ten thousand: 29,05,30,000
Lakh: 29,05,00,000
Ten lakh: 29,00,00,000
Crore: 29,00,00,000
Number with all nearest 5,00,00,000
4,99,99,500 to 5,00,00,499 (1,000 such numbers).
Estimating Sums (Page 11)
4,63,128 + 4,19,682
(a) Both correct, Estu closer.
(b) > 8,50,000 (both >4,00,000).
(c) < 8,83,128 (second <4,20,000).
(d) 8,82,810
14,63,128 - 4,90,020
(a) Both correct, Roxie closer.
(b) > 9,50,000 (14 lakh - 5 lakh = 9 lakh).
(c) > 9,63,128 (first >14 lakh).
(d) 9,73,108
Population Table (Page 12)
1. General observation
Populations grew from 2001 to 2011, Mumbai largest.
2. Title
“Population Growth in Major Indian Cities (2001-2011)”
3. Pune 2011 increase
31,15,431; increase 5,76,958 ≈ 6 lakh.
4. Most increase
Bengaluru (41,24,644).
5. Almost doubled
Bengaluru, Hyderabad, Ahmedabad, Surat, Pune, Jaipur.
6. Multiply Patna by?
1,24,42,373 / 16,84,222 ≈ 7.4 (8 times).
Multiplication Shortcuts (Page 13)
1. Quick products
(a) 2×1768×50 = 1,76,800
(b) 72×125 = 9,000
(c) 125×40×8×25 = 10,00,000
2. Products by 25
(a) 300
(b) 6,000
(c) 30,000
(d) 30,000
(e) 4,80,000 × 25 = 1,20,00,000
How Long is the Product? (Page 14)
Patterns
11×11 = 121
111×111 = 12321
1111×1111 = 1234321
66×61 = 4026
666×661 = 440226
6666×6661 = 44402226
3×5 = 15
33×35 = 1155
333×335 = 111555
101×101 = 10201
102×102 = 10404
103×103 = 10609
Number of Digits in Product (Page 15)
Roxie correct (99×99 = 9801 (4 digits), 10×10 = 100 (3 digits).
3-digit × 3-digit: Yes, 100×100 = 10,000 (5 digits).
4-digit × 2-digit: Yes, 1000×10 = 10,000 (5 digits).
Patterns in Table
5-digit × 5-digit = 9 or 10 digits
8-digit × 3-digit = 10 or 11 digits
12-digit × 13-digit = 24 or 25 digits
Fascinating Facts (Page 16)
1250×380 = 4,75,000 (kirtanas)
2100×70,000 = 14,70,00,000 (Earth-Sun km)
6400×62,500 = 4,00,00,000 (Amazon litres/sec)
Division Facts (Page 17)
13,95,000 ÷ 150 = 9,300 (train journey km)
10,50,00,000 ÷ 700 = 1,50,000 (blue whale kg)
52,00,00,00,000 ÷ 130 = 40,00,00,00,000 (plastic waste tonnes)
Did You Ever Wonder (Page 18)
Mumbai in buses: 1 lakh × 50 = 50 lakh < 1.24 crore (no).
Titanic ships: 5,000 × 2,500 = 1.25 crore > 1.24 crore (yes).
100km/day to Moon: 3,84,400 / 100 = 3,844 days ≈ 10.5 years (no in 10 years).
1000km/day to Sun: 15,00,00,000 / 1000 = 1,50,000 days ≈ 410 years (no in lifetime).
Assumptions
(a) 1 lakh × 5g = 5 lakh g = 500kg (yes, liftable? No, too heavy).
(b) 250/min × 1440 = 3,60,000 > 1 million? No, 3.6 lakh/day.
(c) 1/sec × 86,400 = 86,400 < 10 lakh (no).
Figure it Out (Page 19)
(a) 98,765,4321
(b) Even: 1234567890
2. Seventy three lakh twenty five thousand eight hundred ninety one (31 letters).
3. 9876543210 (exchange any makes bigger).
4. 4555555555 (largest).
5. Eight, nine.
6. Digits
(a) 1000th digit: 1 in 100.
(b) 1 millionth digit in 333,333.
(c) 5000th '5' in 5,000.
7. Button clicks
(a) 2+8 = 10
(b) 9+2+1 = 12
(c) 12+0+5 = 17
(d) 6+5+3 = 14
(e) 7+0+2+5+7 = 21
8. 10,000 lakhs = 1 billion.
9. Largest sum
98765 + 43210 = 1,41,975
10. Close to numbers
(a) 70,000 + 30,000 + 10,000 = 1,10,000
(b) 1,50,000 + 70,000 - 20,000 = 2,00,000
(c) 1,50,000 + 4,00,000 - 20,000 = 5,30,000
(d) 1,50,000 × 8 + 5,000 = 12,05,000
(e) 1,50,000 × 14 - 5,000 = 20,95,000
11. 1,80,000 coins (180m × 1000mm).
12. 12,000 / 1000 = 12 days.
13. 13,560 / 11 = 1,232.7 km/day; /264 hours = 51.36 km/hr.
14. Bald: 4,500 / 40 = 112.5 times; Everest: 8,850 / 40 = 221.25; Plane: 10,000 / 40 = 250.
Puzzle Time (Page 23)
Toothpick Digits
5108: 5+2+2+4 = 13 sticks.
1. 42,019 = 23 sticks.
2. 42,078, 42,079, etc.
3. 42,019 → 421,019 (biggest).
4. 142,019, 412,019, etc.
1. 63,890 = 5+4+5+2+4 = 20 sticks.
2. 88,078, 88,078, etc.
1. e.g., 88888 (20 sticks).
2. 9999999999 (60 sticks? Wait, 24 sticks max: 8888 (16 sticks), etc. Largest: 8888888888 (50 sticks, but for 24: 8888 (16), need to adjust).
3. Smallest: 1111111111 (20 sticks).
1. Chintamani population 2011: 75,000 less than 1 lakh?
1,00,000 - 75,000 = 25,000 less.
2. 2024: 1,06,000 more than 1 lakh?
1,06,000 - 1,00,000 = 6,000 more.
3. Increase from 2011 to 2024?
1,06,000 - 75,000 = 31,000 increase.
Statue vs Building
180 - 40 = 140m taller.
Waterfall vs Building
450 - 40 = 410m taller.
Floors for Waterfall
450 / 4 = 112.5 ≈ 113 floors.
Write in words
(a) Three lakh six hundred
(b) Five lakh four thousand eighty five
(c) Twenty seven lakh thirty thousand
(d) Seventy lakh fifty three thousand one hundred thirty eight
Write numbers
(a) 1,23,456
(b) 4,07,704
(c) 50,05,050
(d) 10,00,235
Land of Tens (Page 5)
1. Thoughtful Thousands (+1000)
(b) 10 times
(c) 53 times
(d) 90 times
(e) 100 times
(g) 100
2. Tedious Tens (+10)
(a) 50 times
(b) 78 times
(c) 100 times
(d) 370 times
(e) 1000 times
(f) 10,000 times
3. Handy Hundreds (+100)
(a) 4 times
(b) 37 times
(c) 100 times
(d) 530 times
(e) 900 times
(f) 976 times
(g) 1000 times
(i) 100
(j) 1000
(k) Yes, numbers not multiples of 100.
Creative Chitti (Page 6)
4. Different way for 5072
(5×1000) + (0×100) + (7×10) + (2×1) = 5072
5. Expressions for numbers
(a) (8×1000) + (3×100) + (0×10) + (0×1)
(b) (4×10000) + (0×1000) + (6×100) + (2×10) + (9×1)
(c) (5×10000) + (6×1000) + (3×100) + (5×10) + (4×1)
(d) (6×10000) + (6×1000) + (6×100) + (6×10) + (6×1)
(e) (3×100000) + (6×10000) + (7×1000) + (8×100) + (1×10) + (3×1)
Systematic Sippy (Page 7)
7. Minimal clicks
(a) 2×10000 + 0×1000 + 8×100 + 0×10 + 0×1
(b) 9×10000 + 2×1000 + 1×100 + 0×10 + 0×1
(c) 1×100000 + 2×10000 + 0×1000 + 5×100 + 0×10 + 0×1
(d) 6×1000000 + 5×100000 + 3×10000 + 0×1000 + 0×100 + 0×10 + 0×1
(e) 7×1000000 + 0×100000 + 2×10000 + 5×1000 + 7×100 + 0×10 + 0×1
Crores (Page 8)
How many zeros in thousand lakh?
1000 × 1,00,000 = 10,00,00,000 (8 zeros).
Figure it Out (Page 9)
1. Read numbers
(a) Indian: Forty lakh fifty thousand six hundred seventy eight; American: Four million fifty thousand six hundred seventy eight.
(b) Indian: Four crore eighty one lakh twenty one thousand six hundred twenty; American: Forty eight million one hundred twenty one thousand six hundred twenty.
(c) Indian: Two crore two lakh twenty thousand two; American: Twenty million two hundred twenty thousand two.
(d) Indian: Twenty four crore sixty eight lakh thirteen thousand five hundred seventy nine; American: Two hundred forty six million eight hundred thirteen thousand five hundred seventy nine.
(e) Indian: Thirty four crore fifty lakh five hundred forty three; American: Three hundred forty five million five hundred forty three.
(f) Indian: One hundred two crore three lakh four thousand fifty; American: One billion twenty million three hundred four thousand fifty.
2. Write numbers
(a) 1,01,01,010
(b) 1,001,001,001
(c) 10,20,30,040
(d) 9,080,700,600
3. Compare
(a) 30,000 < 3,00,000
(b) 5,00,000 < 5,000,000
(c) 8,00,000 < 8,000,000
(d) 640,00,00,000 > 60,000,000,000
Rounding (Page 10)
Situations for rounding
(a) Round up: Ordering food for party (guests 98 → order for 100).
(b) Round down: Budgeting expense (cost 472 → estimate 470).
(c) Either: Approximate distance (120km → 100 or 150).
(d) Exact: Exam marks, bank balance.
Nearest Neighbours (Page 11)
Nearest for 3,87,69,957
Thousand: 3,87,70,000
Ten thousand: 3,87,70,000
Lakh: 3,88,00,000
Ten lakh: 3,90,00,000
Crore: 4,00,00,000
Nearest for 29,05,32,481
Thousand: 29,05,32,000
Ten thousand: 29,05,30,000
Lakh: 29,05,00,000
Ten lakh: 29,00,00,000
Crore: 29,00,00,000
Number with all nearest 5,00,00,000
4,99,99,500 to 5,00,00,499 (1,000 such numbers).
Estimating Sums (Page 11)
4,63,128 + 4,19,682
(a) Both correct, Estu closer.
(b) > 8,50,000 (both >4,00,000).
(c) < 8,83,128 (second <4,20,000).
(d) 8,82,810
14,63,128 - 4,90,020
(a) Both correct, Roxie closer.
(b) > 9,50,000 (14 lakh - 5 lakh = 9 lakh).
(c) > 9,63,128 (first >14 lakh).
(d) 9,73,108
Population Table (Page 12)
1. General observation
Populations grew from 2001 to 2011, Mumbai largest.
2. Title
“Population Growth in Major Indian Cities (2001-2011)”
3. Pune 2011 increase
31,15,431; increase 5,76,958 ≈ 6 lakh.
4. Most increase
Bengaluru (41,24,644).
5. Almost doubled
Bengaluru, Hyderabad, Ahmedabad, Surat, Pune, Jaipur.
6. Multiply Patna by?
1,24,42,373 / 16,84,222 ≈ 7.4 (8 times).
Multiplication Shortcuts (Page 13)
1. Quick products
(a) 2×1768×50 = 1,76,800
(b) 72×125 = 9,000
(c) 125×40×8×25 = 10,00,000
2. Products by 25
(a) 300
(b) 6,000
(c) 30,000
(d) 30,000
(e) 4,80,000 × 25 = 1,20,00,000
How Long is the Product? (Page 14)
Patterns
11×11 = 121
111×111 = 12321
1111×1111 = 1234321
66×61 = 4026
666×661 = 440226
6666×6661 = 44402226
3×5 = 15
33×35 = 1155
333×335 = 111555
101×101 = 10201
102×102 = 10404
103×103 = 10609
Number of Digits in Product (Page 15)
Roxie correct (99×99 = 9801 (4 digits), 10×10 = 100 (3 digits).
3-digit × 3-digit: Yes, 100×100 = 10,000 (5 digits).
4-digit × 2-digit: Yes, 1000×10 = 10,000 (5 digits).
Patterns in Table
5-digit × 5-digit = 9 or 10 digits
8-digit × 3-digit = 10 or 11 digits
12-digit × 13-digit = 24 or 25 digits
Fascinating Facts (Page 16)
1250×380 = 4,75,000 (kirtanas)
2100×70,000 = 14,70,00,000 (Earth-Sun km)
6400×62,500 = 4,00,00,000 (Amazon litres/sec)
Division Facts (Page 17)
13,95,000 ÷ 150 = 9,300 (train journey km)
10,50,00,000 ÷ 700 = 1,50,000 (blue whale kg)
52,00,00,00,000 ÷ 130 = 40,00,00,00,000 (plastic waste tonnes)
Did You Ever Wonder (Page 18)
Mumbai in buses: 1 lakh × 50 = 50 lakh < 1.24 crore (no).
Titanic ships: 5,000 × 2,500 = 1.25 crore > 1.24 crore (yes).
100km/day to Moon: 3,84,400 / 100 = 3,844 days ≈ 10.5 years (no in 10 years).
1000km/day to Sun: 15,00,00,000 / 1000 = 1,50,000 days ≈ 410 years (no in lifetime).
Assumptions
(a) 1 lakh × 5g = 5 lakh g = 500kg (yes, liftable? No, too heavy).
(b) 250/min × 1440 = 3,60,000 > 1 million? No, 3.6 lakh/day.
(c) 1/sec × 86,400 = 86,400 < 10 lakh (no).
Figure it Out (Page 19)
(a) 98,765,4321
(b) Even: 1234567890
2. Seventy three lakh twenty five thousand eight hundred ninety one (31 letters).
3. 9876543210 (exchange any makes bigger).
4. 4555555555 (largest).
5. Eight, nine.
6. Digits
(a) 1000th digit: 1 in 100.
(b) 1 millionth digit in 333,333.
(c) 5000th '5' in 5,000.
7. Button clicks
(a) 2+8 = 10
(b) 9+2+1 = 12
(c) 12+0+5 = 17
(d) 6+5+3 = 14
(e) 7+0+2+5+7 = 21
8. 10,000 lakhs = 1 billion.
9. Largest sum
98765 + 43210 = 1,41,975
10. Close to numbers
(a) 70,000 + 30,000 + 10,000 = 1,10,000
(b) 1,50,000 + 70,000 - 20,000 = 2,00,000
(c) 1,50,000 + 4,00,000 - 20,000 = 5,30,000
(d) 1,50,000 × 8 + 5,000 = 12,05,000
(e) 1,50,000 × 14 - 5,000 = 20,95,000
11. 1,80,000 coins (180m × 1000mm).
12. 12,000 / 1000 = 12 days.
13. 13,560 / 11 = 1,232.7 km/day; /264 hours = 51.36 km/hr.
14. Bald: 4,500 / 40 = 112.5 times; Everest: 8,850 / 40 = 221.25; Plane: 10,000 / 40 = 250.
Puzzle Time (Page 23)
Toothpick Digits
5108: 5+2+2+4 = 13 sticks.
1. 42,019 = 23 sticks.
2. 42,078, 42,079, etc.
3. 42,019 → 421,019 (biggest).
4. 142,019, 412,019, etc.
1. 63,890 = 5+4+5+2+4 = 20 sticks.
2. 88,078, 88,078, etc.
1. e.g., 88888 (20 sticks).
2. 9999999999 (60 sticks? Wait, 24 sticks max: 8888 (16 sticks), etc. Largest: 8888888888 (50 sticks, but for 24: 8888 (16), need to adjust).
3. Smallest: 1111111111 (20 sticks).
4. Different way for 5072
(5×1000) + (0×100) + (7×10) + (2×1) = 5072
5. Expressions for numbers
(a) (8×1000) + (3×100) + (0×10) + (0×1)
(b) (4×10000) + (0×1000) + (6×100) + (2×10) + (9×1)
(c) (5×10000) + (6×1000) + (3×100) + (5×10) + (4×1)
(d) (6×10000) + (6×1000) + (6×100) + (6×10) + (6×1)
(e) (3×100000) + (6×10000) + (7×1000) + (8×100) + (1×10) + (3×1)
7. Minimal clicks
(a) 2×10000 + 0×1000 + 8×100 + 0×10 + 0×1
(b) 9×10000 + 2×1000 + 1×100 + 0×10 + 0×1
(c) 1×100000 + 2×10000 + 0×1000 + 5×100 + 0×10 + 0×1
(d) 6×1000000 + 5×100000 + 3×10000 + 0×1000 + 0×100 + 0×10 + 0×1
(e) 7×1000000 + 0×100000 + 2×10000 + 5×1000 + 7×100 + 0×10 + 0×1
How many zeros in thousand lakh?
1000 × 1,00,000 = 10,00,00,000 (8 zeros).
1. Read numbers
(a) Indian: Forty lakh fifty thousand six hundred seventy eight; American: Four million fifty thousand six hundred seventy eight.
(b) Indian: Four crore eighty one lakh twenty one thousand six hundred twenty; American: Forty eight million one hundred twenty one thousand six hundred twenty.
(c) Indian: Two crore two lakh twenty thousand two; American: Twenty million two hundred twenty thousand two.
(d) Indian: Twenty four crore sixty eight lakh thirteen thousand five hundred seventy nine; American: Two hundred forty six million eight hundred thirteen thousand five hundred seventy nine.
(e) Indian: Thirty four crore fifty lakh five hundred forty three; American: Three hundred forty five million five hundred forty three.
(f) Indian: One hundred two crore three lakh four thousand fifty; American: One billion twenty million three hundred four thousand fifty.
2. Write numbers
(a) 1,01,01,010
(b) 1,001,001,001
(c) 10,20,30,040
(d) 9,080,700,600
3. Compare
(a) 30,000 < 3,00,000
(b) 5,00,000 < 5,000,000
(c) 8,00,000 < 8,000,000
(d) 640,00,00,000 > 60,000,000,000
Situations for rounding
(a) Round up: Ordering food for party (guests 98 → order for 100).
(b) Round down: Budgeting expense (cost 472 → estimate 470).
(c) Either: Approximate distance (120km → 100 or 150).
(d) Exact: Exam marks, bank balance.
Nearest for 3,87,69,957
Thousand: 3,87,70,000
Ten thousand: 3,87,70,000
Lakh: 3,88,00,000
Ten lakh: 3,90,00,000
Crore: 4,00,00,000
Nearest for 29,05,32,481
Thousand: 29,05,32,000
Ten thousand: 29,05,30,000
Lakh: 29,05,00,000
Ten lakh: 29,00,00,000
Crore: 29,00,00,000
Number with all nearest 5,00,00,000
4,99,99,500 to 5,00,00,499 (1,000 such numbers).
4,63,128 + 4,19,682
(a) Both correct, Estu closer.
(b) > 8,50,000 (both >4,00,000).
(c) < 8,83,128 (second <4,20,000).
(d) 8,82,810
14,63,128 - 4,90,020
(a) Both correct, Roxie closer.
(b) > 9,50,000 (14 lakh - 5 lakh = 9 lakh).
(c) > 9,63,128 (first >14 lakh).
(d) 9,73,108
1. General observation
Populations grew from 2001 to 2011, Mumbai largest.
2. Title
“Population Growth in Major Indian Cities (2001-2011)”
3. Pune 2011 increase
31,15,431; increase 5,76,958 ≈ 6 lakh.
4. Most increase
Bengaluru (41,24,644).
5. Almost doubled
Bengaluru, Hyderabad, Ahmedabad, Surat, Pune, Jaipur.
6. Multiply Patna by?
1,24,42,373 / 16,84,222 ≈ 7.4 (8 times).
1. Quick products
(a) 2×1768×50 = 1,76,800
(b) 72×125 = 9,000
(c) 125×40×8×25 = 10,00,000
2. Products by 25
(a) 300
(b) 6,000
(c) 30,000
(d) 30,000
(e) 4,80,000 × 25 = 1,20,00,000
How Long is the Product? (Page 14)
Patterns
11×11 = 121
111×111 = 12321
1111×1111 = 1234321
66×61 = 4026
666×661 = 440226
6666×6661 = 44402226
3×5 = 15
33×35 = 1155
333×335 = 111555
101×101 = 10201
102×102 = 10404
103×103 = 10609
Number of Digits in Product (Page 15)
Roxie correct (99×99 = 9801 (4 digits), 10×10 = 100 (3 digits).
3-digit × 3-digit: Yes, 100×100 = 10,000 (5 digits).
4-digit × 2-digit: Yes, 1000×10 = 10,000 (5 digits).
Patterns in Table
5-digit × 5-digit = 9 or 10 digits
8-digit × 3-digit = 10 or 11 digits
12-digit × 13-digit = 24 or 25 digits
Fascinating Facts (Page 16)
1250×380 = 4,75,000 (kirtanas)
2100×70,000 = 14,70,00,000 (Earth-Sun km)
6400×62,500 = 4,00,00,000 (Amazon litres/sec)
Division Facts (Page 17)
13,95,000 ÷ 150 = 9,300 (train journey km)
10,50,00,000 ÷ 700 = 1,50,000 (blue whale kg)
52,00,00,00,000 ÷ 130 = 40,00,00,00,000 (plastic waste tonnes)
Did You Ever Wonder (Page 18)
Mumbai in buses: 1 lakh × 50 = 50 lakh < 1.24 crore (no).
Titanic ships: 5,000 × 2,500 = 1.25 crore > 1.24 crore (yes).
100km/day to Moon: 3,84,400 / 100 = 3,844 days ≈ 10.5 years (no in 10 years).
1000km/day to Sun: 15,00,00,000 / 1000 = 1,50,000 days ≈ 410 years (no in lifetime).
Assumptions
(a) 1 lakh × 5g = 5 lakh g = 500kg (yes, liftable? No, too heavy).
(b) 250/min × 1440 = 3,60,000 > 1 million? No, 3.6 lakh/day.
(c) 1/sec × 86,400 = 86,400 < 10 lakh (no).
Figure it Out (Page 19)
(a) 98,765,4321
(b) Even: 1234567890
2. Seventy three lakh twenty five thousand eight hundred ninety one (31 letters).
3. 9876543210 (exchange any makes bigger).
4. 4555555555 (largest).
5. Eight, nine.
6. Digits
(a) 1000th digit: 1 in 100.
(b) 1 millionth digit in 333,333.
(c) 5000th '5' in 5,000.
7. Button clicks
(a) 2+8 = 10
(b) 9+2+1 = 12
(c) 12+0+5 = 17
(d) 6+5+3 = 14
(e) 7+0+2+5+7 = 21
8. 10,000 lakhs = 1 billion.
9. Largest sum
98765 + 43210 = 1,41,975
10. Close to numbers
(a) 70,000 + 30,000 + 10,000 = 1,10,000
(b) 1,50,000 + 70,000 - 20,000 = 2,00,000
(c) 1,50,000 + 4,00,000 - 20,000 = 5,30,000
(d) 1,50,000 × 8 + 5,000 = 12,05,000
(e) 1,50,000 × 14 - 5,000 = 20,95,000
11. 1,80,000 coins (180m × 1000mm).
12. 12,000 / 1000 = 12 days.
13. 13,560 / 11 = 1,232.7 km/day; /264 hours = 51.36 km/hr.
14. Bald: 4,500 / 40 = 112.5 times; Everest: 8,850 / 40 = 221.25; Plane: 10,000 / 40 = 250.
Puzzle Time (Page 23)
Toothpick Digits
5108: 5+2+2+4 = 13 sticks.
1. 42,019 = 23 sticks.
2. 42,078, 42,079, etc.
3. 42,019 → 421,019 (biggest).
4. 142,019, 412,019, etc.
1. 63,890 = 5+4+5+2+4 = 20 sticks.
2. 88,078, 88,078, etc.
1. e.g., 88888 (20 sticks).
2. 9999999999 (60 sticks? Wait, 24 sticks max: 8888 (16 sticks), etc. Largest: 8888888888 (50 sticks, but for 24: 8888 (16), need to adjust).
3. Smallest: 1111111111 (20 sticks).
Extra Practice Questions (2M, 3M, 5M)
40+ questions with solutions, categorized by marks for exam prep.
2-Mark Questions
1. What is 1 lakh in numbers?
1,00,000
2. How many days in 100 years (ignore leap)?
36,500
3. Chintamani 2011 population less than lakh?
25,000
4. Statue of Unity height?
180m
5. Write 3,00,600 in words.
Three lakh six hundred
6. +100 button for 400?
4 times
7. 1 crore zeros?
7
8. Round 470 down to hundred.
400
9. Nearest thousand for 6,72,85,183?
6,72,85,000
10. Mumbai population 2011?
1,24,42,373
11. 25 × 12 = ?
300
12. 11 × 11 = ?
121
13. Kirtanas by Purandaradāsa?
4,75,000
14. Train journey km?
9,300
15. Blue whale weight kg?
1,50,000
3-Mark Questions
1. 3 varieties/day in 100 years?
365 × 100 × 3 = 1,09,500 > 1 lakh (yes).
2. Population increase Chintamani?
31,000
3. Waterfall floors?
450 / 4 = 112.5 ≈ 113
4. Write 1,23,456 words.
One lakh twenty three thousand four hundred fifty six
5. +10 for 1 lakh?
10,000 times
6. Indian vs American for 1,00,000
Indian: One lakh; American: One hundred thousand
7. Round up example.
732 guests → 750 sweets
8. Estimate 4,63,128 + 4,19,682
Approx 8,80,000
9. Pune increase
5,76,958 ≈ 6 lakh
10. 72 × 125
9,000 (72 × 1000 / 8)
11. Digits in 3-digit × 3-digit
5 or 6 digits
12. Amazon litres/sec
4,00,00,000
13. Moon travel 100km/day
3,844 days ≈ 10.5 years
14. 1 lakh sheets 5g
500kg (heavy)
15. Toothpick 5108 sticks
13
5-Mark Questions
1. Explain Indian place value with example.
Chart: Crores, Lakhs, Thousands, Hundreds, Tens, Units. Example: 1,23,45,678 = 1 crore 23 lakh 45 thousand 678. Commas: 3-2-2 from right.
2. Compare Indian and American systems.
Indian: Lakh (1,00,000), Crore (1,00,00,000). American: Million (1,000,000), Billion (1,000,000,000). Example table.
3. Rounding situations (4 examples).
Up: Party food. Down: Cost estimate. Either: Distance. Exact: Marks.
4. Multiplication by 25 shortcut with example.
×100 / 4. Example: 72 × 25 = 1,800.
5. Digits in product rule with proof.
Min n+m-1 (10^{n-1} × 10^{m-1} = 10^{n+m-2}). Max n+m (99... × 99... ≈ 10^n × 10^m).
6. Population analysis (3 cities).
Bengaluru doubled, Mumbai grew 4 lakh, etc.
7. Land of Tens full explanation.
Teaches place value through adding multiples.
8. Fascinating fact calculation (2).
Kirtanas, Earth-Sun.
9. Thought experiment (buses).
1 lakh buses × 50 = 50 lakh < Mumbai 1.24 crore (no).
10. Puzzle toothpick largest 24 sticks.
888888 (24 sticks, number 888,888).
Common Mistakes & How to Avoid
Mistake 1: Place Value Commas
Wrong: 1,00000 (lakh).
Avoid: Remember Indian: 1,00,000 (3-2-2).
Mistake 2: Zeros Count
Think lakh has 6 zeros.
Avoid: 1 lakh = 1 followed by 5 zeros.
Mistake 3: Rounding Wrong Way
Round cost up.
Avoid: Round down for estimates, up for safety.
Mistake 4: Multiplication Digits
Think always n+m digits.
Avoid: Range n+m-1 to n+m.
Mistake 5: Estimation
Add rounded separately.
Avoid: Round each, then operate, check range.
Quick Revision One-Pager & Mind Map
| Topic | Key Points |
|---|---|
| Large Numbers | Lakh: 1,00,000; Crore: 1,00,00,000 |
| Place Value | Indian: 3-2-2 commas; American: 3-3-3 |
| Rounding | Up for more, down for less |
| Estimation | Nearest thousand/lakh for quick calc |
| Multiplication | By 5: ×10/2; By 25: ×100/4 |
| Digits in Product | n-digit × m-digit: n+m-1 to n+m |
Mind Map
Central: Large Numbers
- Scale: Lakh days = 274 years
- Systems: Indian (lakh, crore) vs American (million, billion)
- Operations: Add zeros for ×10/100; Shortcuts for 5/25
- Approximation: Round, estimate sums
- Applications: Population, distances, facts
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