📘 Unit 1: LARGE NUMBERS AROUND US — Answer Key (Pages 46–84)
📄 Pages 46–50: Introduction & 1.1 A Lakh Varieties!
Guess (p.48): If Surya tastes 1 new rice variety every day for 100 years (ignoring leap years):
365 × 100 = 36,500 varieties — this is much less than 1,00,000 (one lakh), so he would NOT be able to taste all the varieties.
Fill in the pattern boxes (p.49):
| The largest 3-digit number is | 999 |
| The smallest 4-digit number is | 1,000 |
| The largest 4-digit number is | 9,999 |
| The smallest 5-digit number is | 10,000 |
| The largest 5-digit number is | 99,999 |
| The smallest 6-digit number is | 1,00,000 |
Skip-counting chain (p.49): 99,995 → 99,996 → 99,997 → 99,998 → 99,999 → 1,00,000 → 1,00,001
Ratnam's question (p.50): Eating 2 varieties a day for 100 years: 2 × 365 × 100 = 73,000 (still less than 1 lakh).
(?) 3 varieties a day for 100 years: 3 × 365 × 100 = 1,09,500 — this is MORE than 1 lakh, so yes, all lakh varieties could be tasted.
(?) Choose a number for y: (Sample) If y = 100 years, days = 365 × 100 = 36,500, which is 63,500 less than one lakh. (Answers vary with the value of y chosen.)
✏️ Page 51: Figure it Out - 1.1
1. 1,00,000 − 75,000 = 25,000 less than one lakh.
2. 1,06,000 − 1,00,000 = 6,000 more than one lakh.
3. 1,06,000 − 75,000 = 31,000 increase in population from 2011 to 2024.
📄 Pages 52–53: Getting a Feel of Large Numbers
(Ramu is 1 m tall; each floor of his building ≈ 4 m; Statue of Unity ≈ 180 m ≈ 4 × building height, so building height ≈ 45 m)
(?) Which is taller — Statue of Unity or the building? How much taller?
The Statue of Unity is taller, by about 180 − 45 = 135 m.
(?) How much taller is Kunchikal waterfall (450 m) than Ramu's building?
450 − 45 = 405 m taller.
(?) How many floors should Ramu's building have to be as high as the waterfall?
450 ÷ 4 = ≈113 floors.
(Note: since some population figures on p.53 are faint in the scan, students should substitute their book's printed figures into the same subtraction/estimation method shown in Q.1–3 of Figure it Out 1.1 above.)
✏️ Page 54: Reading and Writing Numbers
(?) Is a lakh big or small? Both views are correct depending on comparison — a lakh is large compared to everyday counts (days in a life, people in a line) but small compared to a stadium's capacity or hairs on our heads. (Open discussion — accept reasoned answers.)
Write in words:
(a) 3,00,600 → Three lakh six hundred
(b) 5,04,085 → Five lakh four thousand eighty five
(c) 27,30,000 → Twenty seven lakh thirty thousand
(d) 70,53,138 → Seventy lakh fifty three thousand one hundred thirty eight
📄 Page 55: Indian Place Value Notation
(a) One lakh twenty three thousand four hundred and fifty six → 1,23,456
(b) Four lakh seven thousand seven hundred and four → 4,07,704
(c) Fifty lakhs five thousand and fifty → 50,05,050
(d) Ten lakhs two hundred and thirty five → 10,00,235
🔢 Pages 56–57: 1.2 Land of Tens
1. Tedious Tens (only +10 button)
(a) Five hundred → 50 times
(b) 780 → 78 times
(c) 1000 → 100 times
(d) 3700 → 370 times
(e) 10,000 → 1,000 times
(f) One lakh → 10,000 times
(g) Pressed 435 times → number shown = 4,350
2. Handy Hundreds (only +100 button)
(a) Four hundred → 4 times
(b) 3,700 → 37 times
(c) 10,000 → 100 times
(d) Fifty three thousand → 530 times
(e) 90,000 → 900 times
(f) 97,600 → 976 times
(g) 1,00,000 → 1,000 times
(h) Pressed 582 times → number shown = 58,200
(i) Hundreds needed to make ten thousand → 100
(j) Hundreds needed to make one lakh → 1,000
(k) "There are numbers Tedious Tens/Thoughtful Thousands can't show but I can" — This statement is FALSE. Every multiple of 100 (which Handy Hundreds shows) is also a multiple of 10, so Tedious Tens (+10) can show every number Handy Hundreds can — and more (e.g. 15, 25). So there's nothing Handy Hundreds can show that Tedious Tens cannot.
3. Thoughtful Thousands (only +1000 button)
(a) Three thousand → 3 times (given)
(b) 10,000 → 10 times
(c) Fifty three thousand → 53 times
(d) 90,000 → 90 times
(e) One lakh → 100 times
(f) Pressed 153 times → number shown = 1,53,000
(g) Thousands needed to make one lakh → 100
4. Creative Chitti (+1,+10,+100,+1000,+10000,+100000,+1000000)
Getting 321: +10 pressed 32 times (320) + 1 pressed once = 321 ✔ Yes, this works.
Alternative: +100 pressed 2 times (200) + 10 pressed 12 times (120) + 1 pressed once (1) = 321 ✔ This also works.
Fill the 5072 table (two different ways):
| Buttons | Way 1 | Way 2 |
|---|---|---|
| +10,00,000 | 0 | 0 |
| +1,00,000 | 0 | 0 |
| +10,000 | 0 | 0 |
| +1,000 | 5 | 3 |
| +100 | 50 | 20 |
| +10 | 7 | 0 |
| +1 | 2 | 72 |
(a) (50×100)+(7×10)+(2×1)=5072 (b) (3×1000)+(20×100)+(72×1)=5072
(?) A different way to get 5072: (5×1000)+(0×100)+(7×10)+(2×1) = 5072
✏️ Page 58: Figure it Out - 1.2
Two ways to make each number using button clicks:
(a) 8300 = (8×1000)+(3×100) = (83×100)
(b) 40629 = (4×10000)+(0×1000)+(6×100)+(2×10)+(9×1) = (40×1000)+(6×100)+(29×1)
(c) 56354 = (5×10000)+(6×1000)+(3×100)+(5×10)+(4×1) = (56×1000)+(3×100)+(54×1)
(d) 66666 = (6×10000)+(6×1000)+(6×100)+(6×10)+(6×1) = (66×1000)+(6×100)+(66×1)
(e) 367813 = (3×1,00,000)+(6×10000)+(7×1000)+(8×100)+(1×10)+(3×1) = (367×1000)+(8×100)+(13×1)
Creative Chitti's questions:
(a) Largest 3-digit number with exactly 30 clicks: use +100 nine times (900), +10 eight times (80), +1 thirteen times (13) → 900+80+13 = 993 (9+8+13=30 clicks).
Smallest 3-digit number with exactly 30 clicks: +10 eight times (80), +1 twenty-two times (22) → 80+22 = 102 (8+22=30 clicks).
(b) Yes — 997 can also be made with a different number of clicks, e.g. (9×100)+(8×10)+(17×1) = 997, using 9+8+17 = 34 clicks (instead of 25).
🔢 Pages 59–60: Systematic Sippy & Figure it Out - 1.3
(?) Fewest clicks for 5072 and 8300:
5072 → (5×1000)+(0×100)+(7×10)+(2×1) → 5+0+7+2 = 14 clicks
8300 → (8×1000)+(3×100) → 8+3 = 11 clicks
1. Fewest clicks for the Page-58 numbers:
| Number | Fewest Clicks (sum of digits) |
|---|---|
| 8300 | 11 |
| 40629 | 21 |
| 56354 | 23 |
| 66666 | 30 |
| 367813 | 28 |
2. Connection: The smallest number of clicks always equals the sum of the digits of the number.
3. Why the least-click expressions give Indian place value notation: Because each digit is pressed exactly the number of times equal to its own value (e.g. digit 5 in the hundreds place needs the +100 button pressed 5 times) — this is exactly what "place value" means: digit × place value, added together.
📄 Pages 61–63: 1.3 Of Crores and Crores!
(?) How many zeros does a thousand lakh have?
1,000 lakh = 1,000 × 1,00,000 = 10,00,00,000 (ten crore) → 8 zeros.
Reading 9876501234:
(a) Indian system: 9,87,65,01,234 → 9 arab 87 crore 65 lakh 1 thousand two hundred thirty four
(b) American system: 9,876,501,234 → 9 billion 876 million 501 thousand two hundred thirty four
✏️ Page 63: Figure it Out - 1.4
1. Number names (Indian & American):
| Number | Indian System | American System |
|---|---|---|
| (a) 4050678 | 40,50,678 — Forty lakh fifty thousand six hundred seventy eight | 4,050,678 — Four million fifty thousand six hundred seventy eight |
| (b) 48121620 | 4,81,21,620 — Four crore eighty one lakh twenty one thousand six hundred twenty | 48,121,620 — Forty eight million one hundred twenty one thousand six hundred twenty |
| (c) 20022002 | 2,00,22,002 — Two crore twenty two thousand two | 20,022,002 — Twenty million twenty two thousand two |
| (d) 246813579 | 24,68,13,579 — Twenty four crore sixty eight lakh thirteen thousand five hundred seventy nine | 246,813,579 — Two hundred forty six million eight hundred thirteen thousand five hundred seventy nine |
| (e) 345000543 | 34,50,00,543 — Thirty four crore fifty lakh five hundred forty three | 345,000,543 — Three hundred forty five million five hundred forty three |
| (f) 1020304050 | 1,02,03,04,050 — One arab two crore three lakh four thousand fifty | 1,020,304,050 — One billion twenty million three hundred four thousand fifty |
2. Indian place value notation:
(a) One crore one lakh one thousand ten → 1,01,01,010
(b) One billion one million one thousand one → 1,00,10,01,001
(c) Ten crore twenty lakh thirty thousand forty → 10,20,30,040
(d) Nine billion eighty million seven hundred thousand six hundred → 9,08,07,00,600
3. Compare using <, >, =:
(a) 30 thousand < 3 lakh
(b) 500 lakh > 5 million (500 lakh = 5,00,00,000; 5 million = 50,00,000)
(c) 800 thousand < 8 million
(d) 640 crore < 60 billion (640 crore = 6.4 billion)
🔢 Pages 64–69: 1.4 Exact and Approximate Values
(?) Round up / round down / either is okay / exact needed — sample situations:
(b) Round down: Announcing a discounted price to sound attractive (₹499 said as "around ₹450–470").
(c) Either is okay: Describing a crowd size in casual conversation ("about 500 people").
(d) Exact numbers needed: Giving someone's marks on a report card, or money in a bank transaction.
Round each number to the nearest hundred/thousand as printed in your textbook copy — use this method: look at the digit just right of the place you are rounding to; if it is 5 or more, round up; if less than 5, round down. Apply this rule to each number listed in your book's Q.1 and Q.3 on page 65.
Nearest Neighbours (p.66–67)
Example given: For 6,72,85,183 —
| Nearest thousand | 6,72,85,000 |
| Nearest ten thousand | 6,72,90,000 |
| Nearest lakh | 6,73,00,000 |
| Nearest ten lakh | 6,70,00,000 |
| Nearest crore | 7,00,00,000 |
(?) Find the five nearest neighbours:
(a) 3,87,69,957
| Nearest thousand | 3,87,70,000 |
| Nearest ten thousand | 3,87,70,000 |
| Nearest lakh | 3,88,00,000 |
| Nearest ten lakh | 3,90,00,000 |
| Nearest crore | 4,00,00,000 |
(b) 29,05,32,481
| Nearest thousand | 29,05,32,000 |
| Nearest ten thousand | 29,05,30,000 |
| Nearest lakh | 29,05,00,000 |
| Nearest ten lakh | 29,10,00,000 |
| Nearest crore | 29,00,00,000 |
Math Talk (?): A number whose all five nearest neighbours are 5,00,00,000 must lie within 500 of 5,00,00,000 (since "nearest thousand" is the tightest condition). So the number can be anywhere from 4,99,99,501 to 5,00,00,500 — that gives 1,000 possible numbers (all other roundings to ten-thousand/lakh/ten lakh/crore are automatically satisfied within this narrow range).
Estimating sums & differences (p.68) — Hasantika & Srestha
1. 4,63,128 + 4,19,682 (exact = 8,82,810)
(a) Srestha's estimate (near 9,00,000, less than 9,00,000) is closer to the actual sum.
(b) The sum is greater than 8,50,000 — because 4,63,128 is already more than half of 8,50,000's pair-share, and both addends round up past the halfway mark.
(c) The sum is less than 8,83,128 — because 4,19,682 is less than 4,20,000.
(d) Exact value = 8,82,810
2. 14,63,128 − 4,90,020 (exact = 9,73,108)
(a) Hasantika's estimate (near 10,00,000, less than 10,00,000) is closer to the actual difference.
(b) The difference is greater than 9,50,000.
(c) The difference is greater than 9,63,128 — because 4,90,020 is less than 5,00,000.
(d) Exact value = 9,73,108
Over-estimate / Under-estimate (p.69): An over-estimate is obtained when we round a number UP, giving a value larger than the actual value. An under-estimate is obtained when we round a number DOWN, giving a value smaller than the actual value. Apply this rule using the exact figures printed in your own textbook copy for the specific numbers in this section.
📄 Pages 70–71: Populations of Cities — Questions
1. General observation: Almost every city's population increased from 2001 to 2011; metro cities like Mumbai, Delhi, Bengaluru, and Hyderabad show the largest populations, and cities such as Bengaluru, Surat, and Vadodara show very fast growth.
2. Population of Pune in 2011 ≈ 31,15,431, approximately 31,15,000. Increase compared to 2001 (25,38,473): 31,15,431 − 25,38,473 = ≈5,77,000 increase.
3. City with the highest increase (2001→2011): Bengaluru — from 43,01,326 to 84,25,970, an increase of about 41,24,644 (the largest jump in the table).
4. Cities whose population almost doubled: Bengaluru (43 lakh → 84 lakh), Surat (24 lakh → 44 lakh), and Vadodara (17 lakh → 35 lakh) show close to double growth.
5. Multiply Patna's population to reach Mumbai's: Mumbai (1,24,42,373) ÷ Patna (16,84,222) ≈ 7.4, so multiplying Patna's population by about 7 to 8 times gives a number close to Mumbai's.
🔢 Pages 72–76: Fascinating Facts about Large Numbers
1250 × 380 = 4,75,000 — the number of kirtanas composed by Purandaradasa.
Follow-up (open/discussion): If he composed 4,75,000 songs over a lifetime of composing, the exact years and starting age depend on the assumed composing period — students may explore e.g. "if he composed for 50 years, that's 4,75,000 ÷ 50 = 9,500 songs per year."
2100 × 70,000 = 14,70,00,000 km — the approximate Earth–Sun distance (close to the actual ~14.96 crore km).
6400 × 62,500 = 40,00,00,000 litres per second — the amount of water the Amazon discharges into the Atlantic every second.
13,95,000 ÷ 150 = 9,300 km — the length of the Moscow–Vladivostok train journey.
10,50,00,000 ÷ 700 = 1,50,000 kg — the weight an adult blue whale can weigh.
52,00,00,00,000 ÷ 130 = 40,00,00,000 (4 crore) tonnes — approximate global plastic waste in 2021 (as per the figures given in the textbook).
Questions on the fact section (p.73):
1. Study the pattern of the numbers → they all involve multiplication or division by large round numbers to reach interesting large facts.
2. Compare population of India in 2011 and 2024 → population increased substantially (over 15 crore) in this period as per Census/estimate data.
3. Difference between 2001 and 2011 population as per your table → use subtraction on the figures in your printed textbook.
4. Explore and share own large number facts → open-ended, e.g., number of blinks a person makes in a year (~1.2 crore).
5. Compare a building's height with a well-known landmark → open-ended, using the "how many times bigger" method shown on page 52.
Veda Numbers (p.76–77)
Tridasati = Trimsat = 3 × 10 = 30
Ekatrimsat (eka + trimsat) = 30 + 1 = 31
Parardha (Yajurveda) = 1012 = 1 lakh crore
Tallakshana (Buddha's count) = 1053
Mahayuga (Ramayana) = 1062
These place-value naming exercises show how ancient Bharat named extremely large powers of 10, long before modern "million/billion/trillion" naming.
📄 Pages 77–79: 1.6 Did You Ever Wonder…?
(?) Can Mumbai's population (1 crore 24 lakh+) fit into 5000 Titanic-sized ships (2500 passengers each)?
5000 × 2,500 = 1,25,00,000 (1 crore 25 lakh) — this is just slightly MORE than Mumbai's population (1,24,42,373), so yes, it would just about fit.
Rakshitha's Moon question: Distance Earth–Moon = 3,84,400 km, travelling 100 km/day:
In 1 year: 100 × 365 = 36,500 km
In 10 years: 36,500 × 10 = 3,65,000 km — this is MORE than 3,84,400 km? No — 3,65,000 km is actually less than 3,84,400 km, so she would not quite reach the Moon in 10 years at this pace (she'd need about 10.5 years).
(?) Reach the Sun in a lifetime at 1000 km/day?
Sun distance ≈ 14,70,00,000 km (from earlier fact). In 80 years: 1000 × 365 × 80 = 2,92,00,000 km — far short of the distance to the Sun, so no, not possible in one lifetime at this speed.
(?) Reasonable-assumption questions:
(a) A single sheet of paper (5 g) — one lakh sheets = 5 × 1,00,000 = 5,00,000 g = 500 kg — far too heavy for a person to lift at once.
(b) 250 babies born every minute → in a day: 250 × 60 × 24 = 3,60,000 — this is less than a million (10,00,000), so a million babies are NOT born in a single day at that rate.
(c) Counting 1 coin per second for 1 million coins: 10,00,000 seconds ÷ (60×60×24) = ≈11.6 days — so no, you cannot count 1 million coins in a single day.
✏️ Pages 79–83: Figure it Out - 1.5
1. Using digits 0–9 exactly once (first digit ≠ 0), 10-digit number:
(a) Largest multiple of 5 → 98,76,54,32,10 (i.e. 9876543210 — already ends in 0)
(b) Smallest even number → 10,23,45,67,98 (i.e. 1023456798)
2. A 7-digit number name with the maximum letters (sample answer): 77,77,777 → "Seventy seven lakh seventy seven thousand seven hundred seventy seven" — this uses the long word "seventy" four times, giving one of the longest possible number names.
3. A 9-digit number where exchanging any two digits gives a bigger number must have all its digits strictly increasing from left to right (each digit smaller than the one after it) with no repeats and no zero (0 can't be a leading digit). The only such 9-digit number is 1,23,45,6789 (123456789) — so only 1 such number exists.
4. Striking 10 digits from 12345123451234512345 (20 digits) to get the largest possible 10-digit number:
Using a greedy "keep the biggest digits" method → 55,34,51,2345 (i.e., 5534512345).
5. (Try This) Finding two consecutive numbers whose English names share no common letter is a fun open exploration — most nearby number-name pairs (zero-one, one-two, four-five, etc.) do share at least one letter. Students should try checking number names systematically (starting from small numbers and going higher) to discover a pair with nothing in common — this is meant for exploration and discussion rather than a single fixed answer.
6. Digits written as 123456789101112...:
(a) The 1000th digit is 3, occurring in the number 370.
(b) The millionth digit is 1, occurring in the number 1,85,185.
(c) The digit '5' is written for the 5000th time in the number 13,495 (as its last/units digit).
7. Calculator with only '+10,000' and '+100' buttons — expression for each number:
(a) 20,800 = (2×10,000) + (8×100)
(b) 92,100 = (9×10,000) + (21×100)
(c) 1,20,500 = (12×10,000) + (5×100)
(d) 65,30,000 = (653×10,000) + (0×100)
(e) 70,25,700 = (702×10,000) + (57×100)
8. How many lakhs make a billion? 1 billion = 1,00,00,00,000 ÷ 1,00,000 = 10,000 lakhs.
9. Cards 1–9 for largest sum / smallest difference (sample method using two 3-digit numbers):
Smallest possible difference: Make the two numbers as close as possible by keeping their hundreds (and tens) digits nearly equal — e.g. 407 − 396 = 11.
10. Using cards 4000, 13000, 300, 70000, 1,50,000, 20, 5 (each used once) to get close to a target:
(a) 1,10,000: 4000 × (20+5) + 13000 = 1,13,000 (given example)
(b) 2,00,000: 13000 × (20−5) + 4000 + 300 = 1,99,300 (close approximation)
(c)–(e) (Try This — open exploration; students should experiment with combinations of the given cards and operations to get as close as possible to 5,80,000 / 12,45,000 / 20,90,800.)
11. Coins (1 mm thick each) stacked to match the Statue of Unity (180 m = 1,80,000 mm):
1,80,000 ÷ 1 = 1,80,000 coins.
12. Albatross flying 12,000 km at 900–1000 km/day:
12,000 ÷ 1000 = 12 days; 12,000 ÷ 900 ≈ 13.3 days → approximately 12 to 14 days.
13. Bar-tailed godwit — 13,560 km in 11 days:
Per day: 13,560 ÷ 11 ≈ 1,233 km/day
Per hour: 1,233 ÷ 24 ≈ 51.4 km/hour.
14. Comparing heights to Ramu's building (≈45 m, based on the earlier Statue of Unity comparison):
Bald eagles (4500–6000 m): 4500÷45 to 6000÷45 = ≈100 to 133 times
Mount Everest (8850 m): 8850÷45 ≈ 197 times
Aeroplanes (10,000–12,800 m): 10000÷45 to 12800÷45 = ≈222 to 284 times
📄 Page 84: Additional Application Problems & Summary
This page extends the ideas of the chapter with real-life money and counting contexts (crorepati amounts, net worth brackets, and pattern-based counting puzzles). Students should apply the same tools used throughout the chapter:
1 lakh = 1,00,000 (1 followed by 5 zeros)
1 crore = 1,00,00,000 (1 followed by 7 zeros)
1 arab (100 crore) = 1,00,00,00,000 (1 followed by 9 zeros) = 1 billion
1 kharab (100 arab) = 1,00,00,00,00,000 (1 followed by 11 zeros)
Apply subtraction, multiplication, division, and rounding — exactly as practised in Figure it Out 1.1 to 1.5 above — to solve each numbered problem on this page using the exact figures printed in your own textbook copy.
📌 SUMMARY (Page 84)
- 1 lakh = 1,00,000 (1 followed by 5 zeroes)
- 1 crore = 1,00,00,000 (1 followed by 7 zeroes)
- 1 million = 10,00,000 (1 followed by 6 zeroes) = 10 lakh
- 1 arab = 1,00,00,00,000 (1 followed by 9 zeroes) = 100 crore = 1 billion
- We round numbers up or down to make them easier to work with and understand.
- We can get a sense of large numbers by comparing them to smaller, more familiar quantities.
- Factorising and regrouping numbers can make multiplication easier.
End of Unit 1 Answer Key — Large Numbers Around Us (Class 7 Mathematics, AP SCERT)
