Large Numbers Around Us Class 7 Solutions Ganita Prakash Maths Chapter 1✦ Step-by-step
HBSE 7th Class Maths Solutions Chapter 1 Large Numbers Around Us (NCERT Ganita Prakash) — every question worked out step by step. Tap Solve step by step to reveal the working one line at a time.
Class 7 Maths Chapter 1 Large Numbers Around Us Solutions
Key ideas used in this chapter
Indian systemones, tens, hundreds, thousands, lakhs, crores
Lakh & crore1 lakh = 1,00,000; 1 crore = 1,00,00,000
Internationalthousand, million (10 lakh), billion (100 crore)
Estimationround to a nearby 1000 / lakh to check an answer
Reading and Writing Numbers (Pages 4–5)
Q.Write in words
(a) 3,00,600 (b) 5,04,085 (c) 27,30,000 (d) 70,53,138
How
Read each comma-group: crore, lakh, thousand, then hundreds/tens/ones.
(a)
3 lakh | 00 thousand | 600 ⇒ Three lakh six hundred
(b)
5 lakh | 04 thousand | 085 ⇒ Five lakh four thousand eighty-five
(c)
27 lakh | 30 thousand | 000 ⇒ Twenty-seven lakh thirty thousand
(d)
70 lakh | 53 thousand | 138 ⇒ Seventy lakh fifty-three thousand one hundred thirty-eight
Q.Write in figures
(a) One lakh twenty-three thousand four hundred fifty-six (b) Four lakh seven thousand seven hundred four (c) Fifty lakh five thousand fifty (d) Ten lakh two thousand thirty-five
(a)
1 lakh, 23 thousand, 456 ⇒ 1,23,456
(b)
4 lakh, 07 thousand, 704 ⇒ 4,07,704
(c)
50 lakh, 05 thousand, 050 ⇒ 50,05,050
(d)
10 lakh, 02 thousand, 035 ⇒ 10,02,035
Figure It Out (Page 3)
Q1–3Chintamani population
Population was 75,000 (2011) and 1,06,000 (2024). (1) How much less than a lakh is 75,000? (2) How much more than a lakh is 1,06,000? (3) Increase from 2011 to 2024?
Q1
1,00,000 − 75,000: 100 thousand − 75 thousand = 25 thousand ⇒ 25,000 less
Q2
1,06,000 − 1,00,000 = 6,000 more
Q3
1,06,000 − 75,000 = 31,000 increase
Getting a Feel of Large Numbers (Pages 3–4)
Q.Heights (from the picture)
Somu is 1 m tall; each floor is 4× his height and the building has 10 floors. Find the building's height, then compare with the Statue of Unity (180 m) and Kunchikal waterfall (450 m). How many floors would equal the waterfall?
Building
each floor = 4 × 1 = 4 m; 10 floors ⇒ 10 × 4 = 40 m
vs Statue
180 − 40 = 140 m ⇒ the Statue is 140 m taller
vs Waterfall
450 − 40 = 410 m ⇒ the waterfall is 410 m taller
Floors needed
450 ÷ 4 = 112.5 ⇒ at least 113 floors
1.2 Land of Tens (Pages 5–6)
Q1–3Counting button presses
How many presses of +1000, +10 or +100 give the target? (each press = one division)
Idea
presses = target ÷ button value.
+1000
10,000÷1000=10; 53,000÷1000=53; 1,00,000÷1000=100 ⇒ 100 thousands make a lakh
+10
500÷10=50; 3700÷10=370; 1,00,000÷10=10,000
+100
97,600÷100=976; 1,00,000÷100=1000 ⇒ 100 hundreds = ten thousand, 1000 hundreds = a lakh
Q4–5Chitti's ways
(Q4) Two ways to make 321. (Q5) A different way to get 5072.
321 way 1
(32×10) + (1×1) = 320 + 1 = 321
321 way 2
(2×100)+(12×10)+(1×1) = 200+120+1 = 321
5072
(5×1000)+(7×10)+(2×1) = 5000+70+2 = 5072
Figure It Out (Pages 6–8)
Q1Two ways each
Write two button-click expressions for (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813.
(a)
(8×1000)+(3×100) or (83×100)
(b)
(4×10000)+(6×100)+(2×10)+(9×1) or (406×100)+(29×1)
(c),(d)
(56×1000)+(354×1); (66×1000)+(666×1)
(e)
(367×1000)+(813×1) or (3×100000)+(67×1000)+(813×1)
many correct answers.
Q2Exactly 30 presses
(a) Largest and smallest 3-digit number in exactly 30 presses. (b) Make 997 with a different number of clicks.
(a) largest
(9×100)+(8×10)+(13×1)=993; clicks 9+8+13=30
(a) smallest
(8×10)+(22×1)=102; clicks 8+22=30
(b)
(8×100)+(19×10)+(7×1)=997; clicks 8+19+7=34
Q1–3Fewest clicks & the pattern
Fewest clicks for 8300, 40629, 56354, 66666, 367813 — and why it matches the place-value form.
8300 / 40629
8+3 = 11; 4+6+2+9 = 21
56354 / 66666 / 367813
23; 30; 3+6+7+8+1+3 = 28
Pattern
fewest clicks = the sum of the digits — using the biggest button per place is the place-value expansion.
1.3 Of Crores and Crores — Figure It Out (Page 9)
Q1Indian & International names
Write in both notations and names: (a) 4050678 (b) 48121620 (c) 20022002 (d) 246813579 (e) 345000543 (f) 1020304050.
How
Indian: group as 2-2-2-3 from the right; International: group in 3s.
(a)
40,50,678 / 4,050,678 — forty lakh fifty thousand six hundred seventy-eight
(b),(c)
4,81,21,620 / 48,121,620; 2,00,22,002 / 20,022,002
(d),(e)
24,68,13,579 / 246,813,579; 34,50,00,543 / 345,000,543
(f)
1,02,03,04,050 / 1,020,304,050 — one billion twenty million three hundred four thousand fifty
Q2Write in Indian notation
(a) One crore one lakh one thousand ten (b) One billion one million one thousand one (c) Ten crore twenty lakh thirty thousand forty (d) Nine billion eighty million seven hundred thousand six hundred
(a),(c)
1,01,01,010; 10,20,30,040
(b)
1 billion+1 million+1 thousand+1 = 1,00,10,01,001
(d)
9,08,07,00,600 (9,080,700,600)
Q3Compare
(a) 30 thousand __ 3 lakh (b) 500 lakh __ 5 million (c) 800 thousand __ 8 million (d) 640 crore __ 60 billion
(a)
30,000 vs 3,00,000 ⇒ <
(b)
500 lakh = 5,00,00,000; 5 million = 50,00,000 ⇒ >
(c)
8,00,000 vs 80,00,000 ⇒ <
(d)
640 crore = 6.4 billion vs 60 billion ⇒ <
1.4 Exact and Approximate Values (Pages 11–13)
Q.Nearest neighbours
Round 3,87,69,957 to the nearest thousand, ten-thousand, lakh, ten-lakh and crore.
How
Look at the digit just after the rounding place: 5 or more → round up.
thousand, ten-thousand
3,87,70,000; 3,87,70,000
lakh, ten-lakh, crore
3,88,00,000; 3,90,00,000; 4,00,00,000
Q.Exact values
Find (1) 4,63,128 + 4,19,682 and (2) 14,63,128 − 4,90,020, and check them against an estimate.
(1) estimate
≈ 4,63,000 + 4,20,000 = 8,83,000
(1) exact
4,63,128 + 4,19,682 = 8,82,810
(2) estimate
≈ 15,00,000 − 5,00,000 = 10,00,000
(2) exact
14,63,128 − 4,90,020 = 9,73,108
PopulationCity table (Pages 12–13)
From the table: Pune's increase (2001: 25,38,473 → 2011: 31,15,431); which city increased most; multiplier to take Patna (16,84,222) to Mumbai (1,24,42,373).
Pune
31,15,431 − 25,38,473 = 5,76,958 ≈ 5.8 lakh
Most increase
Bengaluru: 84,25,970 − 43,01,326 = 41,24,644 — the highest
Patna → Mumbai
1,24,42,373 ÷ 16,84,222 ≈ 7.4 ⇒ multiply by about 7
1.5 Patterns in Products — Figure It Out (Page 14)
Q1Quick products
(a) 2×1768×50 (b) 72×125 (c) 125×40×8×25
(a)
pair 2×50 = 100; then 100×1768 = 1,76,800
(b)
125 = \(\frac{1000}{8}\); 72×\(\frac{1000}{8}\) = 9×1000 = 9000
(c)
(125×8)×(40×25) = 1000×1000 = 10,00,000
Q2Quick products
(a) 25×12 (b) 25×240 (c) 250×120 (d) 2500×12 (e) __ × __ = 12,00,00,000
Trick
25 = \(\frac{100}{4}\)
(a),(b)
\(\frac{100}{4}\)×12 = 100×3 = 300; \(\frac{100}{4}\)×240 = 100×60 = 6000
(c),(d)
250×120 = 30,000; 2500×12 = 30,000
(e)
25,000 × 4800 = 12,00,00,000
Figure It Out (Pages 19–21)
Q1Digits 0–9 once
(a) Largest multiple of 5 (b) smallest even number.
(a)
a multiple of 5 ends in 0 or 5; largest = digits descending ending in 0 ⇒ 9876543210
(b) Step 1
smallest 10-digit (no leading 0) = 1023456789
(b) Step 2
make it even by swapping the last two digits ⇒ 1023456798
Q2, Q3Letters & swaps
(Q2) 7-digit number whose name has the most letters. (Q3) 9-digit number where any swap makes it bigger.
Q2
use 7 (“seven”, 5 letters) throughout ⇒ 77,77,777 = 60 letters
Q3
123456789 — already smallest with increasing digits, so any swap enlarges it
Q4Strike out digits
Strike out 10 digits from 12345123451234512345 to leave the largest number.
Idea
Greedily keep the largest possible leading digits while leaving enough digits to fill 10 places.
Answer
5,53,45,12,345
Q5, Q6Letters & digit counting
(Q5) Two consecutive number-names with no shared letter? (Q6) 1000th digit, millionth digit, and the 5000th ‘5’ when writing 1, 2, 3, …
Q5
one&two share o, two&three share t,e, … every consecutive pair shares a letter ⇒ none
Q6 (a)
1–9: 9 digits, 10–99: 180 ⇒ 189; 1000−189 = 811 = 270×3 + 1 ⇒ 1st digit of 370 ⇒ 3
Q6 (b),(c)
millionth digit is in 1,85,185; the 5000th ‘5’ is at 13,995
Q7+10,000 and +100
Expression for the number of clicks: (a) 20,800 (b) 92,100 (c) 1,20,500 (d) 65,30,000 (e) 70,25,700.
How
split into ten-thousands and hundreds; clicks = sum of the two counts.
(a),(b)
(2×10000)+(8×100) ⇒ 10; (9×10000)+(21×100) ⇒ 30
(c)
(12×10000)+(5×100) ⇒ 12+5 = 17
(d),(e)
(653×10000) ⇒ 653; (702×10000)+(57×100) ⇒ 759
Q8, Q9Lakhs & cards
(Q8) How many lakhs make a billion? (Q9) With cards 1–9, largest sum and smallest difference of a 7-digit and a 5-digit number.
Q8
\(\frac{1{,}000{,}000{,}000}{1{,}00{,}000}=10{,}000\) lakhs
Q9 largest sum
98,76,543 + 98,765 = 99,75,308
Q9 smallest diff
12,34,567 − 98,765 = 11,35,802
Q10Number cards
Cards 4000, 13000, 300, 70000, 150000, 20, 5 (each once). Get close to (a) 1,10,000 (b) 2,00,000 (c) 5,80,000 (d) 12,45,000.
(a)
70000 + 4000×5 + 13000 = 70000+20000+13000 = 1,03,000
(b)
150000 + 70000 − 4000×5 = 220000 − 20000 = 2,00,000
(c)
70000×5 + 150000 + 4000×20 = 350000+150000+80000 = 5,80,000
(d)
70000×20 − 150000 − 4000 − 300×5 = 12,44,500
many close combinations exist.
Q11Coins & Statue
How many 1 mm-thick coins stack to the height of the Statue of Unity (180 m)?
Step 1
180 m = 180 × 1000 mm = 1,80,000 mm
Step 2
1,80,000 ÷ 1 = 1,80,000 coins
Q12–13Migration
(Q12) 12,000 km trip at 900–1000 km/day — days? (Q13) Godwit flew 13,560 km in ~11 days — km per day and per hour.
Q12
12,000÷1000 = 12 days; 12,000÷900 ≈ 13.3 ⇒ about 12–14 days
Q13 / day
13,560 ÷ 11 ≈ 1233 km
Q13 / hour
11 days = 264 hours; 13,560 ÷ 264 ≈ 51 km
Q14Compared to a 40 m building
How many times taller than the 40 m building are: eagle flight 4500–6000 m, Mount Everest 8850 m, aeroplanes 10,000–12,000 m?
Eagle
4500÷40 = 112.5 to 6000÷40 = 150 ⇒ ~112–150×
Everest
8850 ÷ 40 ≈ 221×
Aeroplane
10,000÷40 = 250 to 12,000÷40 = 300 ⇒ ~250–300×