Class 7 Maths Ganita Prakash Chapter 1 Solutions (NCERT 2026–27) – Large Numbers Around Us

These Class 7 Maths Ganita Prakash Chapter 1 solutions cover Large Numbers Around Us from the new NCF-2023 textbook (Reprint 2026–27). Find worked answers, place-value diagrams, checked button-click and number-card puzzles, rounding examples and toothpick activities. Use the textbook alongside these explanations.

Class: 7 Subject: Mathematics Book: Ganita Prakash (Part I) Chapter: 1 Exercises: Figure it Out (p.3, p.6, p.7, p.9, p.14, p.19–21) Session: 2026–27
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Chapter 1 Overview

Chapter 1 of Ganita Prakash, Large Numbers Around Us, follows Roxie and Estu as they get a feel for really big numbers — starting from one lakh (1,00,000) and building up to crores and arabs. The chapter teaches the Indian place value system (the 3-2-2-2 comma pattern) alongside the American/International system (the 3-3-3 pattern with millions and billions), reading and writing large number names, the “Land of Tens” calculator puzzles, exact vs approximate values and rounding to the nearest thousand/lakh/crore, comparing city populations, and clever patterns in products that make multiplication quicker. The solutions below explain the textbook exercises and selected explorations with checked working.

Key Concepts & Definitions

One lakh: the smallest 6-digit number, written 1,00,000 — it is 1 followed by 5 zeroes, and equals a hundred thousand (100 × 1000).

One crore: a hundred lakhs, written 1,00,00,000 — it is 1 followed by 7 zeroes.

One arab: a hundred crores, written 1,00,00,00,000 — it is 1 followed by 9 zeroes; it is the same as one billion.

Indian place value system: commas group digits as 3-2-2-2… from the right (thousands, lakhs, crores). Used in India, Nepal, Sri Lanka, Pakistan, Bangladesh and more.

American / International system: commas group digits as 3-3-3… from the right (thousands, millions, billions). 1 million = 10,00,000 = ten lakhs; 1 billion = 100 crore.

Rounding up: approximating to a number that is more than the actual value (e.g. 732 → 750).

Rounding down: approximating to a number that is less than the actual value (e.g. ₹470 → ₹450).

Nearest neighbours: the nearest thousand, ten thousand, lakh, ten lakh and crore of a number.

4,81,21,620 and 48,121,620 represent the same value.
4,81,21,620 and 48,121,620 represent the same value.

Important Formulas & Patterns (Chapter 1)

Place-value links: 1 lakh = 100 thousand  •  1 crore = 100 lakh = 10 million  •  1 arab = 100 crore = 1 billion.

Zeroes: 1 lakh = 1 followed by 5 zeroes; 1 crore = 1 followed by 7 zeroes; 1 million = 1 followed by 6 zeroes; 1 arab/billion = 1 followed by 9 zeroes.

Fewest button clicks: the minimum number of +1, +10, +100… clicks equals the sum of the digits of the number, and the click expression is exactly its Indian place-value expansion.

Multiply by 5: n × 5 = n × (10 ÷ 2) = (n ÷ 2) × 10. Multiply by 25 = ×(100 ÷ 4); by 125 = ×(1000 ÷ 8).

Digits in a product: a (p-digit) × (q-digit) number has either (p + q − 1) or (p + q) digits.

Stage-wise large calculation: break long multiplications/divisions into easy stages (e.g. per day → per year → per 10 years).

Figure it Out — A Lakh Varieties (Page 3)

1. According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?

SOLUTION One lakh = 1,00,000. 1,00,000 − 75,000 = 25,000. ∴ 75,000 is 25,000 (twenty-five thousand) less than one lakh.

2. The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?

SOLUTION 1,06,000 − 1,00,000 = 6,000. ∴ 1,06,000 is 6,000 (six thousand) more than one lakh.

3. By how much did the population of Chintamani increase from 2011 to 2024?

SOLUTION Increase = 2024 population − 2011 population = 1,06,000 − 75,000. 1,06,000 − 75,000 = 31,000. ∴ the population increased by 31,000 (thirty-one thousand).

Figure it Out — Land of Tens (Page 6)

For each number given below, write expressions for at least two different ways to obtain the number through button clicks (Creative Chitti has buttons +1, +10, +100, +1000, +10000, +100000, +1000000). Think like Chitti and be creative.

(a) 8300

SOLUTION Way 1: (8 × 1000) + (3 × 100) = 8000 + 300 = 8300. Way 2: (83 × 100) = 8300, i.e. press +100 eighty-three times.

(b) 40629

SOLUTION Way 1: (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) = 40000 + 600 + 20 + 9 = 40629. Way 2: (40 × 1000) + (62 × 10) + (9 × 1) = 40000 + 620 + 9 = 40629.

(c) 56354

SOLUTION Way 1: (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) = 56354. Way 2: (56 × 1000) + (35 × 10) + (4 × 1) = 56000 + 350 + 4 = 56354.

(d) 66666

SOLUTION Way 1: (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) = 66666. Way 2: (66 × 1000) + (66 × 10) + (6 × 1) = 66000 + 660 + 6 = 66666.

(e) 367813

SOLUTION Way 1: (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1) = 367813. Way 2: (36 × 10000) + (78 × 100) + (1 × 10) + (3 × 1) = 360000 + 7800 + 10 + 3 = 367813.

Creative Chitti has some questions for you — (a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make? (b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?

SOLUTION(a) Smallest: 102 = 8 × 10 + 22 × 1, using 8 + 22 = 30 presses. Largest: 993 = 8 × 100 + 19 × 10 + 3 × 1, using 30 presses.Why these are the limits: start with thirty +1 presses, giving 30. Each replacement by +10 adds 9; each replacement by +100 adds 99. Every total is therefore 30 plus a multiple of 9. The first such total at least 100 is 102; the last below 1,000 is 993. The expressions above show both are possible.(b) 997 = 9 × 100 + 9 × 10 + 7 × 1 needs 25 clicks. Replacing one hundred by ten tens gives 8 × 100 + 19 × 10 + 7 × 1, or 34 clicks.
Replacing a +1 click by +10 adds 9; replacing it by +100 adds 99. This explains the limits 102 and 993.
Replacing a +1 click by +10 adds 9; replacing it by +100 adds 99. This explains the limits 102 and 993.

Figure it Out — Fewest Button Clicks (Page 7)

Systematic Sippy (buttons +1, +10, +100, +1000, +10000, +100000) wants to use as few clicks as possible.

1. For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression. (numbers: 8300, 40629, 56354, 66666, 367813)

SOLUTION The fewest clicks come from pressing each place-value button as many times as that digit — i.e. the Indian place-value expansion. 8300 = (8 × 1000) + (3 × 100) → 8 + 3 = 11 clicks. 40629 = (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) → 4 + 6 + 2 + 9 = 21 clicks. 56354 = (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) → 5 + 6 + 3 + 5 + 4 = 23 clicks. 66666 = (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) → 6 + 6 + 6 + 6 + 6 = 30 clicks. 367813 = (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1) → 3 + 6 + 7 + 8 + 1 + 3 = 28 clicks.

2. Do you see any connection between each number and the corresponding smallest number of button clicks?

SOLUTION Yes — the smallest number of button clicks is exactly the sum of the digits of the number. (For 8300: 8+3+0+0 = 11; for 40629: 4+0+6+2+9 = 21; for 56354: 23; for 66666: 30; for 367813: 28.)

3. If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.

SOLUTION Each place-value button (+1, +10, +100, …) adds exactly one unit of that place. To build a number with the fewest presses you should add each place value the exact number of times shown by its digit — no more, no less. Using ten +1 presses (10 clicks) instead of one +10 press (1 click) only wastes clicks. So the minimal click recipe is “digit at each place × that place value”, which is precisely the Indian place-value expansion of the number.
The digit at each place tells us how many times to press that place-value button.
The digit at each place tells us how many times to press that place-value button.

Figure it Out — Of Crores and Crores (Page 9)

1. Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems: (a) 4050678   (b) 48121620   (c) 20022002   (d) 246813579   (e) 345000543   (f) 1020304050

SOLUTION (a) Indian: 40,50,678 = forty lakh fifty thousand six hundred seventy eight. American: 4,050,678 = four million fifty thousand six hundred seventy eight. (b) Indian: 4,81,21,620 = four crore eighty one lakh twenty one thousand six hundred twenty. American: 48,121,620 = forty eight million one hundred twenty one thousand six hundred twenty. (c) Indian: 2,00,22,002 = two crore twenty two thousand two. American: 20,022,002 = twenty million twenty two thousand two. (d) Indian: 24,68,13,579 = twenty four crore sixty eight lakh thirteen thousand five hundred seventy nine. American: 246,813,579 = two hundred forty six million eight hundred thirteen thousand five hundred seventy nine. (e) Indian: 34,50,00,543 = thirty four crore fifty lakh five hundred forty three. American: 345,000,543 = three hundred forty five million five hundred forty three. (f) Indian: 1,02,03,04,050 = one arab two crore three lakh four thousand fifty (= 102 crore 3 lakh 4 thousand 50). American: 1,020,304,050 = one billion twenty million three hundred four thousand fifty.

2. Write the following numbers in Indian place value 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

SOLUTION (a) 1 crore + 1 lakh + 1 thousand + 10 = 1,01,01,010. (b) 1 billion = 100 crore, 1 million = 10 lakh, 1 thousand, 1 one → 1,00,00,00,000 + 10,00,000 + 1,000 + 1 = 1,00,10,01,001. (c) 10 crore + 20 lakh + 30 thousand + 40 = 10,00,00,000 + 20,00,000 + 30,000 + 40 = 10,20,30,040. (d) 9 billion = 900 crore, 80 million = 8 crore, 7 hundred thousand = 7 lakh, 6 hundred → 9,00,00,00,000 + 8,00,00,000 + 7,00,000 + 600 = 9,08,07,00,600.

3. Compare and write ‘<’, ‘>’ or ‘=’: (a) 30 thousand ____ 3 lakhs (b) 500 lakhs ______ 5 million (c) 800 thousand ____ 8 million (d) 640 crore ______ 60 billion

SOLUTION (a) 30 thousand = 30,000; 3 lakhs = 3,00,000. So 30,000 < 3,00,000. (b) 500 lakhs = 5,00,00,000 (5 crore); 5 million = 50,00,000 (50 lakh). So 500 lakhs > 5 million. (c) 800 thousand = 8,00,000 (8 lakh); 8 million = 80,00,000 (80 lakh). So 800 thousand < 8 million. (d) 640 crore = 6,40,00,00,000; 60 billion = 60 × 100 crore = 6000 crore = 60,00,00,00,000. So 640 crore < 60 billion.

Figure it Out — Did You Ever Wonder…? (Page 19–21)

1. Using all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-digit number, write the — (a) Largest multiple of 5 (b) Smallest even number

SOLUTION (a) A multiple of 5 must end in 0 or 5. To make it largest, put big digits first and end in 0 (keeping 5 available for a high place). Largest = 9876543210 (ends in 0, a multiple of 5). (b) An even number must end in an even digit. To make it smallest, start with the smallest non-zero digit (1) and arrange the rest in ascending order ending in an even digit. Smallest = 1023456798 (ends in 8, so even; first digit is 1, and 0 is placed in the second position which is allowed).

2. The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 43 letters. Give a 7-digit number name which has the maximum number of letters.

SOLUTIONOne maximum example is 77,77,777: “seventy seven lakhs seventy seven thousand seven hundred seventy seven”. Ignoring spaces and hyphens, the count is 12 + 5 + 12 + 8 + 5 + 7 + 12 = 61 letters. This follows the question’s plural “lakhs” and omits “and”. Using “lakh” gives 60.Among numbers below 100, the longest names have 12 letters, such as seventy three, seventy seven and seventy eight. The longest hundreds digit name has 5 letters (three, seven or eight). Maximising each group independently proves this is a maximum; several numbers tie.

3. Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?

SOLUTIONThe digits must be strictly increasing from left to right. Equal digits would leave the number unchanged when swapped; a larger digit before a smaller one would allow a swap that reduces the number.Zero cannot appear because it would have to be first. The only nine available digits are 1–9, so 123456789 is the only answer.

4. Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.

SOLUTIONKeep the digits at positions 5, 10, 13, 14, 15, 16, 17, 18, 19 and 20. They give 5534512345. The other ten positions are deleted.Choose the largest possible next digit while leaving enough digits to finish. The first two 5s can be kept, but choosing the third 5 next would leave too few digits to make a ten-digit result. After the first two 5s, only two more deletions remain: remove the next 1 and 2.
Cross out positions 1–4, 6–9, 11 and 12. The largest remaining number is 5534512345.
Cross out positions 1–4, 6–9, 11 and 12. The largest remaining number is 5534512345.

5. The words ‘zero’ and ‘one’ share letters ‘e’ and ‘o’. The words ‘one’ and ‘two’ share a letter ‘o’, and the words ‘two’ and ‘three’ also share a letter ‘t’. How far do you have to count to find two consecutive numbers which do not share an English letter in common?

SOLUTIONYou will not find such a pair in ordinary English whole-number names. Adjacent small number names share a letter: zero/one share o, one/two share o, two/three share t, three/four share r, four/five share f, five/six share i, six/seven share s, seven/eight share e and eight/nine share e.Within a ten, hundred or larger named group, consecutive names share the unchanged part. At a change of group, check the boundary: nineteen/twenty share t and n; twenty-nine/thirty share t and y; ninety-nine/one hundred share n and e. At a new power of a thousand, the lower name ends in nine and the next starts with one, sharing n and e. Thus counting farther does not produce the requested pair.

6. Suppose you write down all the numbers 1, 2, 3, 4, …, 9, 10, 11, … The tenth digit you write is ‘1’ and the eleventh digit is ‘0’, as part of the number 10. (a) What would the 1000th digit be? At which number would it occur? (b) What number would contain the millionth digit? (c) When would you have written the digit ‘5’ for the 5000th time?

SOLUTION (a) Digits 1–9 use 9 digits (numbers 1–9). Numbers 10–99 are 90 two-digit numbers = 180 digits, reaching digit 9 + 180 = 189. So far 189 digits used by 99. Three-digit numbers begin at 100; we need digit 1000, i.e. 1000 − 189 = 811 more digits into three-digit numbers. 811 ÷ 3 = 270 remainder 1, so after 270 complete three-digit numbers (100 to 369) we have used 189 + 810 = 999 digits ending at 369. The 1000th digit is the 1st digit of the next number, 370, which is ‘3’. (b) 1-digit: 9 digits; 2-digit: 180 (total 189); 3-digit: 900 numbers × 3 = 2700 (total 2889); 4-digit: 9000 × 4 = 36000 (total 38889); 5-digit: 90000 × 5 = 450000 (total 488889); 6-digit: numbers 100000… The millionth digit needs 1000000 − 488889 = 511111 more digits among 6-digit numbers. 511111 ÷ 6 = 85185 remainder 1, so after 85185 six-digit numbers (100000 to 185184) we reach 488889 + 511110 = 999999 digits; the millionth digit is the 1st digit of 185185, i.e. the number containing it is 185185. (c) The 5,000th occurrence is the final digit of 13,495. Numbers 1–9,999 contribute 4,000 fives. From 10,000–12,999 there are 900 more (300 per block of 1,000). From 13,000–13,399 there are 80; from 13,400–13,489 there are 19. That makes 4,999. The next five is the units digit of 13,495.

7. A calculator has only ‘+10,000’ and ‘+100’ buttons. Write an expression describing the number of button clicks to be made for the following numbers: (a) 20,800   (b) 92,100   (c) 1,20,500   (d) 65,30,000   (e) 70,25,700

SOLUTION Each number = (number of +10,000 clicks) × 10000 + (number of +100 clicks) × 100. (a) 20,800 = (2 × 10000) + (8 × 100) → 2 + 8 = 10 clicks. (b) 92,100 = (9 × 10000) + (21 × 100) → 9 + 21 = 30 clicks. (c) 1,20,500 = (12 × 10000) + (5 × 100) → 12 + 5 = 17 clicks. (d) 65,30,000 = (653 × 10000) + (0 × 100) → 653 clicks. (e) 70,25,700 = (702 × 10000) + (57 × 100) → 702 + 57 = 759 clicks.

8. How many lakhs make a billion?

SOLUTION 1 billion = 1,00,00,00,000 (1 followed by 9 zeroes); 1 lakh = 1,00,000 (1 followed by 5 zeroes). 1 billion ÷ 1 lakh = 109 ÷ 105 = 104 = 10,000 lakhs make a billion.

9. You are given two sets of number cards numbered from 1 – 9. Place a number card in each box below to get the (a) largest possible sum (b) smallest possible difference of the two resulting numbers.

SOLUTIONThe textbook has seven boxes in the upper row and five in the lower row. Use the two sets together: each digit 1–9 is available at most twice, and 0 is unavailable.(a) One largest-sum arrangement is 99,87,654 + 87,654 = 1,00,75,308. Put the two 9s in the two highest places, then the two 8s in the ten-thousands places, and continue with 7s, 6s, 5s and 4s. Exchanging digits at equal place values can give other optimal arrangements.(b) The smallest difference is 11,22,334 − 99,887 = 10,22,447. Give the smallest digits to the largest positive place values in the upper row and the largest digits to the negative place values in the lower row. Each card is used at most twice.
With two copies of each digit 1–9 available, 99,87,654 + 87,654 = 1,00,75,308; 11,22,334 − 99,887 = 10,22,447.
With two copies of each digit 1–9 available, 99,87,654 + 87,654 = 1,00,75,308; 11,22,334 − 99,887 = 10,22,447.

10. You are given some number cards; 4000, 13000, 300, 70000, 150000, 20, 5. Using the cards get as close as you can to the numbers below using any operation you want. Each card can be used only once for making a particular number. (a) 1,10,000: Closest I could make is 4000 × (20 + 5) + 13000 = 1,13,000 (b) 2,00,000: (c) 5,80,000: (d) 12,45,000: (e) 20,90,800:

SOLUTIONThese are valid examples; each listed card is used at most once in an expression. Unused cards are allowed.(a) 13,000 × 20 − 1,50,000 = 1,10,000, exactly.(b) 70,000 × 5 − 1,50,000 = 2,00,000, exactly.(c) First 1,50,000 ÷ 300 = 500; then 70,000 ÷ 500 = 140. Thus 4,000 × [70,000 ÷ (1,50,000 ÷ 300) + 5] = 4,000 × 145 = 5,80,000, exactly.(d) (13,000 + 70,000) × (300 ÷ 20) = 83,000 × 15 = 12,45,000, exactly.(e) 70,000 + [(1,50,000 − 13,000) ÷ 20] × (300 − 5) = 70,000 + 6,850 × 295 = 20,90,750. This is only 50 below the target. It is a close valid answer, not a claim that no closer expression exists.

11. Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick.

SOLUTION Height of the Statue of Unity ≈ 180 metres = 180 × 1000 = 1,80,000 mm. Each coin is 1 mm thick, so number of coins = 1,80,000 ÷ 1 = 1,80,000 coins (one lakh eighty thousand).

12. Grey-headed albatrosses have a roughly 7-feet wide wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900 – 1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?

SOLUTION At about 1000 km per day: 12,000 ÷ 1000 = 12 days. At about 900 km per day: 12,000 ÷ 900 ≈ 13.3, i.e. about 13–14 days. ∴ the trip takes approximately 12 to 14 days.

13. A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560 km from Alaska to Australia without stopping. Its journey started on 13 October 2022 and continued for about 11 days. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.

SOLUTION Per day = 13,560 ÷ 11 ≈ 1233 km → about 1,200 km per day. Per hour = 1233 ÷ 24 ≈ 51 km → about 50 km per hour (or 13,560 ÷ (11 × 24) = 13,560 ÷ 264 ≈ 51 km/h).

14. Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is about 8850 m high. Aeroplanes can fly as high as 10,000 – 12,800 m. How many times bigger are these heights compared to Somu’s building?

SOLUTIONCounting the ground storey and ten storeys above it in the page 3 drawing gives 11 × 4 = 44 m as an approximate building height. Use the same estimate throughout.Bald eagle: 4,500 ÷ 44 ≈ 102.3 and 6,000 ÷ 44 ≈ 136.4, so about 102–136 times the building height.Mount Everest: 8,850 ÷ 44 ≈ 201 times. Aeroplane: 10,000 ÷ 44 ≈ 227.3 to 12,800 ÷ 44 ≈ 290.9, so about 227–291 times.If your classroom uses the rounded building estimate 40 m, the corresponding ratios are 112.5–150, 221.25 and 250–320. State your assumption; 16 m does not represent the illustrated building.
Counting the ground storey and ten storeys above it gives approximately 44 m. This is an estimate from the textbook illustration.
Counting the ground storey and ten storeys above it gives approximately 44 m. This is an estimate from the textbook illustration.

More in-text worked examples

Reading numbers and filling the early patterns (pages 2–5)

The consecutive milestones are 999, 1,000, 9,999, 10,000, 99,999 and 1,00,000. The missing number-line values are 99,997, 99,999 and 1,00,000.

NumberIndian number name
3,00,600Three lakh six hundred
5,04,085Five lakh four thousand eighty-five
27,30,000Twenty-seven lakh thirty thousand
70,53,138Seventy lakh fifty-three thousand one hundred thirty-eight

The number-name questions on page 5 give 1,23,456; 4,07,704; 50,05,050; 10,00,235, respectively.

Single-button calculators (pages 5–6)

CalculatorAnswers in textbook order
Thoughtful Thousands(a) 3; (b) 10; (c) 53; (d) 90; (e) 100 presses; (f) 1,53,000; (g) 100 thousands.
Tedious Tens(a) 50; (b) 78; (c) 100; (d) 370; (e) 1,000; (f) 10,000 presses; (g) 4,350.
Handy Hundreds(a) 4; (b) 37; (c) 100; (d) 530; (e) 900; (f) 976; (g) 1,000 presses; (h) 58,200; (i) 100 hundreds; (j) 1,000 hundreds.

For 321, both 32 × 10 + 1 and 2 × 100 + 12 × 10 + 1 work. For 5,072, use 5 × 1,000 + 7 × 10 + 2 × 1: 14 clicks. Ten presses of +10,00,000 give one crore, with seven zeroes. A thousand lakhs is 10,00,00,000, with eight zeroes; a hundred thousand has five zeroes.

Nearest neighbours (page 11)

Round to nearest3,87,69,95729,05,32,481
Thousand3,87,70,00029,05,32,000
Ten thousand3,87,70,00029,05,30,000
Lakh3,88,00,00029,05,00,000
Ten lakh3,90,00,00029,10,00,000
Crore4,00,00,00029,00,00,000

Round up when ordering enough sweets; round down when estimating how many complete groups fit a budget; either direction may suit a rough crowd estimate. Telephone numbers, account numbers and exact payments must not be rounded.

City populations (pages 12–13)

Use the textbook’s 2001 and 2011 data, not present-day population estimates. A suitable title is “Populations of selected Indian cities in 2001 and 2011”. Most increased; Kolkata decreased from 45,72,876 to 44,86,679.

Pune’s 2011 population was 31,15,431, about 31 lakh. Its increase was 31,15,431 − 25,38,473 = 5,76,958, approximately 6 lakh. Bengaluru had the largest increase in the table: 84,25,970 − 43,01,326 = 41,24,644.

Bengaluru, Hyderabad, Surat and Vadodara are approximately doubled examples (about 1.96, 1.87, 1.84 and 2.10 times respectively). Mumbai ÷ Patna in 2011 is 1,24,42,373 ÷ 16,84,222 ≈ 7.39, so multiplying Patna by about 7 gives a close whole-number estimate.

Large quantities in stages (pages 18–19)

Using the textbook assumptions: 5,000 ships × 2,500 people = 1,25,00,000, enough for the stated Mumbai population, with 57,627 places spare. At 100 km/day, travel in a year is 36,500 km and in ten years 3,65,000 km: 19,400 km short of the Moon’s stated distance.

At 1,000 km/day, 14,70,00,000 km to the Sun would take 1,47,000 days, about 403 years. One lakh sheets at 5 g each weigh 500 kg, too heavy for a person to lift together. At 250 births/minute, a day gives 250 × 60 × 24 = 3,60,000, below a million. At one coin/second, a million coins takes 1,000,000 ÷ 86,400 ≈ 11.57 days without breaks.

Height comparisons (page 3)

Using the illustrated building estimate of 44 m: the textbook’s approximately 180 m statue is 136 m taller; the approximately 450 m waterfall is 406 m taller. At 4 m per storey, 450 ÷ 4 = 112.5 storeys, so 113 full storeys would reach at least that height.

Math Talk & Try This — Answered

These are the in-text Math Talk reflections and Try This / explore tasks in the chapter; the determinate ones are answered, the open ones are guided.

Lifetime of rice varieties (p.2–3) If a person ate 3 varieties of rice every day, will they taste all one lakh varieties in a 100-year lifetime? (Days in y years = 365 × y.) Answer. Days in 100 years ≈ 365 × 100 = 36,500 days. Eating 3 varieties a day gives 3 × 36,500 = 1,09,500 varieties — just over one lakh. So at 3 a day you could (only barely) cross a lakh in 100 years, while at 1 or 2 a day (36,500 or 73,000) you would not reach one lakh.
Math Talk — Why the fewest clicks give place value (p.7) The expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so. Answer. Replacing one +10 click by ten +1 clicks wastes 9 clicks, and similarly for the higher buttons. The cheapest way to build a number is therefore to press each place-value button exactly as many times as that digit — which is precisely the Indian place-value expansion (digit × place value at each position).
Handy Hundreds’ claim (p.6) Handy Hundreds says, “There are some numbers which Tedious Tens and Thoughtful Thousands can’t show but I can.” Is this statement true? Answer. False as worded. Every number made by +100 presses can also be made with +10 presses: replace each +100 with ten +10 presses. For example, 500 takes five +100 presses or fifty +10 presses. Thoughtful Thousands cannot make 500, but Tedious Tens can. Handy Hundreds therefore cannot make a number that both other calculators cannot show.
Math Talk — A number whose five neighbours are all 5,00,00,000 (p.11) I have a number for which all five nearest neighbours (nearest thousand, ten thousand, lakh, ten lakh, crore) are 5,00,00,000. What could the number be? How many such numbers are there? Answer. The number must round to 5,00,00,000 at every level, so it must lie within 500 of 5,00,00,000 (the tightest rounding is to the nearest thousand). So it can be any whole number from 4,99,99,500 to 5,00,00,499 — that is 1000 such numbers (for example 5,00,00,000 itself, or 4,99,99,873).
Math Talk — Why multiplying by 5 = dividing by 2, then ×10 (p.13) Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10? Answer. Because 5 = 10 ÷ 2. So n × 5 = n × (10 ÷ 2) = (n ÷ 2) × 10. Halving first and then multiplying by 10 is often easier, e.g. 116 × 5 = (116 ÷ 2) × 10 = 58 × 10 = 580.
Estimating a sum (p.11) For 4,63,128 + 4,19,682: Roxie says the sum is near and more than 8,00,000; Estu says near and less than 9,00,000. Are these correct? Who is closer? Will the sum be > or < 8,50,000? > or < 8,83,128? Exact value? Answer. Exact sum = 4,63,128 + 4,19,682 = 8,82,810. Both estimates point to the right region; Estu’s (near 9,00,000) is closer. The sum is greater than 8,50,000 (since 8,82,810 > 8,50,000) and less than 8,83,128 (8,82,810 < 8,83,128).
Estimating a difference (p.11) For 14,63,128 − 4,90,020: Roxie says near and less than 10,00,000; Estu says near and more than 9,00,000. Are these correct? Who is closer? > or < 9,50,000? > or < 9,63,128? Exact value? Answer. Exact difference = 14,63,128 − 4,90,020 = 9,73,108. Roxie’s (near 10,00,000, less than it) is correct and closer. The difference is greater than 9,50,000 and greater than 9,63,128 (since 9,73,108 > both).
Quick products by factorising (Figure it Out, p.14) Find quick ways: (a) 2 × 1768 × 50 (b) 72 × 125 [125 = 1000÷8] (c) 125 × 40 × 8 × 25. Also: (a) 25×12 (b) 25×240 (c) 250×120 (d) 2500×12 (e) __×__ = 120000000. Answer. (a) 2 × 50 = 100, so 1768 × 100 = 1,76,800. (b) 72 × 125 = 72 × 1000 ÷ 8 = 72000 ÷ 8 = 9000. (c) 125 × 8 = 1000 and 40 × 25 = 1000, so 1000 × 1000 = 10,00,000.   25 × 12 = 300; 25 × 240 = 6000; 250 × 120 = 30,000; 2500 × 12 = 30,000; and one easy pair is 12,000 × 10,000 = 12,00,00,000 (= 120000000).
How long is the product? (p.14–15) Find the patterns: 11×11, 111×111, …; 66×61, 666×661, …; 3×5, 33×35, …; 101×101, 102×102, 103×103. Answer. 11×11 = 121, 111×111 = 12321, 1111×1111 = 1234321 (a palindrome “pyramid”). 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.
Digits in a product (p.15) Roxie says the product of two 2-digit numbers can only be a 3- or 4-digit number. Is she correct? Complete: 5-digit × 5-digit = __ ; 8-digit × 3-digit = __ ; 12-digit × 13-digit = __. Answer. Yes, Roxie is correct — the smallest is 10 × 10 = 100 (3 digits) and the largest is 99 × 99 = 9801 (4 digits). In general (p-digit) × (q-digit) has (p + q − 1) or (p + q) digits. So 5×5 → 9 or 10 digits; 8×3 → 10 or 11 digits; 12×13 → 24 or 25 digits.
Fascinating facts — products & quotients (p.16–18) Compute: 1250×380; 2100×70,000; 6400×62,500; 13,95,000÷150; 10,50,00,000÷700; 52,00,00,00,000÷130. Answer. 1250 × 380 = 4,75,000 (kīrtanas by Purandaradāsa). 2100 × 70,000 = 14,70,00,000 = 14.7 crore km (Earth–Sun distance). 6400 × 62,500 = 40,00,00,000 = 40 crore litres/second (Amazon discharge). 13,95,000 ÷ 150 = 9,300 km (Moscow–Vladivostok train). 10,50,00,000 ÷ 700 = 1,50,000 kg (blue whale). 52,00,00,00,000 ÷ 130 = 40,00,00,000 = 40 crore tonnes (2021 plastic waste).
Try This — Toothpick Digits (p.23) Using sticks (the digit 7 needs 3 sticks): How many sticks for 5108? Make 42,019 (needs 23 sticks); add two sticks for a bigger number. Make the biggest and smallest number using exactly 24 sticks. Answer. Standard segment costs for digits 0–9 are 6, 2, 5, 5, 4, 5, 6, 3, 7, 6. Thus 5108 needs 20 sticks, and 42,019 needs 23. Adding two sticks can give 42,078 (1→7 and 9→8) or 42,879 (0→8 and 1→7).

Inserting a new digit 1 into 42019 gives the distinct numbers 142019, 412019, 421019, 420119 and 420191. The largest is 4,21,019.

With exactly 24 sticks, the largest whole number is 111111111111: twelve 1s use 24 sticks. No digit uses fewer than two sticks. The smallest is 2008: 5+6+6+7=24. Three digits can use at most 21 sticks, and a four-digit number starting with 1 can use at most 23; starting with 2, choose 0, 0, then 8.

For the four-stick rearrangement of 63,890, one valid larger result is 99,006. Move the lower-left segment of the first 6 to its upper-right (6→9); remove the middle segment of 8 and use it as the upper-left of 3 (8→0, 3→9); move the middle segment of the fourth digit to its lower-left (9→0); move the upper-right of the last 0 to its middle (0→6). These are exactly four moved sticks.
Standard seven-segment digits use 6, 2, 5, 5, 4, 5, 6, 3, 7 and 6 sticks respectively.
Standard seven-segment digits use 6, 2, 5, 5, 4, 5, 6, 3, 7 and 6 sticks respectively.
Three digits can use at most 21 sticks. The smallest valid four-digit number is 2008; twelve 1s give the largest number.
Three digits can use at most 21 sticks. The smallest valid four-digit number is 2008; twelve 1s give the largest number.
Add a middle segment to 0 and a top segment to 1 to make 42,879. No existing stick is moved.
Add a middle segment to 0 and a top segment to 1 to make 42,879. No existing stick is moved.

Common Mistakes to Avoid

Watch out for these

  • Putting commas in the wrong places — the Indian system groups 3-2-2-2 from the right (1,00,000) while the American system groups 3-3-3 (100,000). Don’t mix them.
  • Confusing a million with a lakh: 1 million = 10,00,000 = ten lakhs, not one lakh.
  • Miscounting zeroes: 1 lakh has 5 zeroes, 1 crore has 7, 1 arab/billion has 9.
  • Forgetting that the fewest button clicks equals the sum of the digits, not the number of digits.
  • Rounding the wrong way — rounding up gives a value larger than the actual; rounding down gives a smaller one.
  • In “digits in a product”, forgetting that the answer can be either (p + q − 1) or (p + q) digits, not a fixed count.

Practice MCQs & Assertion–Reason

1. One lakh is the same as:

(a) ten thousand    (b) hundred thousand    (c) ten million    (d) one crore

2. How many zeroes are there in one crore?

(a) 5    (b) 6    (c) 7    (d) 9

3. In the Indian place value system, commas are placed in the pattern (from the right):

(a) 3-3-3    (b) 3-2-2-2    (c) 2-2-2    (d) 4-4-4

4. One million equals:

(a) one lakh    (b) ten lakhs    (c) one crore    (d) hundred lakhs

5. The smallest number of button clicks (using +1, +10, +100…) needed to make a number equals its:

(a) number of digits    (b) sum of digits    (c) largest digit    (d) product of digits

6. How many lakhs make one billion?

(a) 100    (b) 1,000    (c) 10,000    (d) 1,00,000

7. The number 4,81,21,620 in words (Indian system) is:

(a) four crore eighty one lakh twenty one thousand six hundred twenty    (b) forty eight lakh…    (c) four lakh…    (d) forty eight crore…

8. The exact value of 4,63,128 + 4,19,682 is:

(a) 8,72,810    (b) 8,82,810    (c) 8,83,128    (d) 9,00,000

9. The product of two 2-digit numbers can have at most:

(a) 2 digits    (b) 3 digits    (c) 4 digits    (d) 5 digits

10. The nearest lakh of 6,72,85,183 is:

(a) 6,72,85,000    (b) 6,73,00,000    (c) 6,70,00,000    (d) 7,00,00,000

Answer key: 1-(b), 2-(c), 3-(b), 4-(b), 5-(b), 6-(c), 7-(a), 8-(b), 9-(c), 10-(b).

For each Assertion–Reason question, choose: (A) Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion; (B) Both are true but the Reason is not the correct explanation; (C) Assertion is true but Reason is false; (D) Assertion is false but Reason is true.

A-R 1. Assertion: One crore is written as 1,00,00,000.

Reason: One crore is a hundred lakhs and equals 1 followed by 7 zeroes.

A-R 2. Assertion: One million is equal to one lakh.

Reason: In the American system, a million is grouped as 1,000,000.

A-R 3. Assertion: The fewest button clicks to make 8300 with +1, +10, +100… buttons is 11.

Reason: The minimum number of clicks equals the sum of the digits of the number.

A-R 4. Assertion: 10,000 lakhs make one billion.

Reason: One billion has 9 zeroes and one lakh has 5 zeroes, and 109 ÷ 105 = 104.

A-R 5. Assertion: In the Indian place value system, commas are placed uniformly in groups of three from the right.

Reason: The Indian system groups digits as thousands, lakhs and crores.

Answer key: 1-(A), 2-(D), 3-(A), 4-(A), 5-(D).

Quick Revision Summary

  • One lakh = 1,00,000 (1 followed by 5 zeroes); one crore = 1,00,00,000 (1 followed by 7 zeroes); one arab = one billion = 1 followed by 9 zeroes.
  • Indian system groups digits 3-2-2-2 from the right; American/International groups 3-3-3 (thousand, million, billion).
  • 1 million = 10 lakhs; 1 billion = 100 crore = 10,000 lakhs.
  • The fewest place-value button clicks for a number = the sum of its digits, and equals its Indian place-value expansion.
  • Round up (value larger than actual) or round down (value smaller) when only an approximation is needed; find nearest thousand/lakh/crore.
  • Multiply quickly by factorising: ×5 = ÷2 then ×10; ×25 = ×100÷4; ×125 = ×1000÷8.
  • A (p-digit) × (q-digit) product has (p + q − 1) or (p + q) digits; break big calculations into stages.

How to score full marks in this chapter

Always place the commas before reading or writing a number, and state which system (Indian or American) you are using. For button-click questions, write the place-value expansion and add the digits for the fewest clicks. When estimating, say whether you are rounding up or down and by roughly how much, then give the exact answer where asked. Use factorising shortcuts (×5, ×25, ×125) to avoid long multiplication, and break very large calculations into easy stages so each step earns its mark.

Frequently Asked Questions

What is Class 7 Maths Ganita Prakash Chapter 1 about?

Chapter 1, Large Numbers Around Us, covers reading and writing large numbers (lakhs, crores, arabs) in the Indian and American/International systems, the “Land of Tens” button-click puzzles, exact versus approximate values and rounding, comparing city populations, and quick patterns in products.

How many Figure it Out exercises are there in Chapter 1?

There are six “Figure it Out” sets — on page 3 (A Lakh Varieties), page 6 (Land of Tens), page 7 (fewest button clicks), page 9 (Of Crores and Crores) page 14 (quick products) and pages 19–21 (Did You Ever Wonder) — plus several Math Talk and Try This tasks, all solved on this page.

How many zeroes are there in a lakh, a crore and a billion?

One lakh has 5 zeroes (1,00,000), one crore has 7 zeroes (1,00,00,000) and one billion (one arab) has 9 zeroes (1,00,00,00,000). One million has 6 zeroes and equals ten lakhs.

Are these Class 7 Maths Ganita Prakash Chapter 1 solutions free?

Yes. All solutions are free and follow the official NCERT Ganita Prakash (Part I) textbook for the 2026–27 session, with worked exercises and illustrated explanations.

Textbook reference: NCERT Ganita Prakash, Chapter 1 (official PDF). ClearStudy diagrams and worked explanations are original teaching aids.

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