NCERT Solutions for Class 7 Maths Chapter 1: Large Numbers Around Us – Ganita Prakash

Chapter 1 of the Class 7 NCERT Ganita Prakash textbook (Part 1) is titled “Large Numbers Around Us”. It covers reading and writing large numbers, the Indian vs. International (American) numeral systems, comparing large numbers, estimation, and place-value reasoning using patterns. These Class 7 Mathematics Chapter 1 solutions are also useful as quick revision notes before exams.

Below are original, independently verified solutions to the chapter’s key questions.

1.1 A Lakh Varieties!

Q. If you tried one new rice variety every day, could you taste all 1,00,000 (one lakh) varieties in a 100-year lifetime? What about 2 varieties/day, or 3 varieties/day?
Solution: At 1 variety/day: 1,00,000 ÷ 365 ≈ 274 years — far longer than a lifetime, so no. At 2 varieties/day: 1,00,000 ÷ 730 ≈ 137 years — still too long. At 3 varieties/day: 1,00,000 ÷ 1095 ≈ 91 years — this fits within a 100-year lifetime, so at 3 varieties a day, all 1 lakh varieties could be tasted.

Q (Chintamani’s population). The 2011 population of Chintamani was about 75,000, and the estimated 2024 population is 1,06,000. (i) How much less than one lakh is 75,000? (ii) How much more than one lakh is 1,06,000? (iii) By how much did the population increase from 2011 to 2024?
Solution: (i) 1,00,000 − 75,000 = 25,000. (ii) 1,06,000 − 1,00,000 = 6,000. (iii) 1,06,000 − 75,000 = 31,000.

Q (Building heights). Somu is 1 m tall; each floor of a building is about 4 times his height, and the building has 11 floors. The Statue of Unity is 180 m tall and the Kunchikal waterfall is 450 m tall. (a) Find the building’s height. (b) How much taller is the Statue of Unity? (c) How much taller is the waterfall? (d) How many floors would the building need to match the waterfall’s height?
Solution: (a) Height of one floor = 4×1 = 4 m; building height = 11×4 = 44 m. (b) 180 − 44 = 136 m taller. (c) 450 − 44 = 406 m taller. (d) 450 ÷ 4 = 112.5, so the building would need approximately 113 floors.

Reading and Writing Large Numbers

Q. Write in words: (a) 3,00,600 (b) 5,04,085 (c) 27,30,000 (d) 70,53,138
Solution: (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.

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 hundred thirty-five
Solution: (a) 1,23,456 (b) 4,07,704 (c) 50,05,050 (d) 10,00,235

1.2 Land of Tens

Q. Using only a “+1000” button, how many presses to reach: (a) 3,000 (b) 10,000 (c) 53,000 (d) 90,000 (e) 1,00,000? How many thousands make one lakh?
Solution: (a) 3 (b) 10 (c) 53 (d) 90 (e) 100. 100 thousands make one lakh.

Q. Using only a “+100” button: how many presses for 10,000? For one lakh?
Solution: 10,000 ÷ 100 = 100 presses. 1,00,000 ÷ 100 = 1,000 presses — so 1,000 hundreds make one lakh.

Q (Creative Chitti). Write 5,072 using place-value expressions in two different ways.
Solution: (i) (5×1000) + (7×10) + (2×1) = 5072. (ii) (3×1000) + (20×100) + (72×1) = 3000+2000+72 = 5072. Both are valid decompositions of the same number.

1.3 Of Crores and Crores!

Q. How many zeros does a thousand lakh have? How many zeros does a hundred thousand have?
Solution: 1,000 lakh = 1,000 × 1,00,000 = 10,00,00,000 (one crore), which has 8 zeros. 100 thousand = 1,00,000, which has 5 zeros.

Q. Write 4,81,21,620 in both the Indian and American (International) numeral systems, with words.
Solution: Indian system: 4,81,21,620 — Four crore eighty-one lakh twenty-one thousand six hundred twenty. American system: 48,121,620 — Forty-eight million one hundred twenty-one thousand six hundred twenty.

Q. Write 20,022,002 in Indian place-value notation, with words.
Solution: Grouping from the right in the Indian style (3 digits, then pairs of 2): 2,00,22,002 — Two crore twenty-two thousand two.

Q. Compare using >, <, or =: (a) 30 thousand ___ 3 lakh (b) 500 lakh ___ 5 million (c) 800 thousand ___ 8 million (d) 640 crore ___ 60 billion
Solution: (a) 30,000 < 3,00,000 ⇒ <. (b) 500 lakh = 5,00,00,000; 5 million = 50,00,000 ⇒ 5,00,00,000 > 50,00,000 ⇒ >. (c) 8,00,000 < 80,00,000 ⇒ <. (d) 640 crore = 6,40,00,00,000 = 6.4 billion; 60 billion is much larger ⇒ <.

Estimating Sums and Differences

Q. Estimate, then find the exact value of 4,63,128 + 4,19,682.
Solution: Rounding each to the nearest lakh: 5,00,000 + 4,00,000 = 9,00,000 (estimate). Exact sum = 8,82,810 — reasonably close to the 9,00,000 estimate.

Q. Estimate, then find the exact value of 14,63,128 − 4,90,020.
Solution: Rounding: 15,00,000 − 5,00,000 = 10,00,000 (estimate). Exact difference = 9,73,108 — close to the 10,00,000 estimate.

1.5 Patterns in Products — A Multiplication Shortcut

Q. Use a shortcut to compute: (a) 2 × 1768 × 50 (b) 72 × 125 (c) 125 × 40 × 8 × 25
Solution: (a) 2×50 = 100, so 1768×100 = 1,76,800. (b) 125 = 1000/8, so 72×1000/8 = 72000/8 = 9,000. (c) Group as (125×8)×(40×25) = 1000×1000 = 10,00,000.

Q. Compute using factoring shortcuts: (a) 25×12 (b) 25×240 (c) 250×120 (d) 2500×12
Solution: (a) 25×4×3 = 100×3 = 300. (b) 25×4×60 = 100×60 = 6,000. (c) 250×4×30 = 1000×30 = 30,000. (d) 2500×4×3 = 10000×3 = 30,000.

Q (Digit-count patterns). Can the product of two 2-digit numbers ever be more than 4 digits? Can the product of a 3-digit and 3-digit number ever be only 4 digits?
Solution: Two 2-digit numbers range from 10×10=100 (3 digits) to 99×99=9801 (4 digits) — so the product is always 3 or 4 digits, never more. Two 3-digit numbers range from 100×100=10,000 (5 digits) to 999×999=998,001 (6 digits) — so the product is always 5 or 6 digits, never just 4.

Estimation & Reasoning with Very Large Numbers

Q (Titanic comparison). If a ship carries about 2,500 passengers, could 5,000 such ships carry Mumbai’s population of about 1,24,00,000?
Solution: Capacity of 5,000 ships = 5,000 × 2,500 = 1,25,00,000, which is greater than 1,24,00,000. Yes, Mumbai’s population could fit.

Q (Reaching the Moon). If you travel 100 km/day, would you reach the Moon (distance ≈ 3,84,400 km) in 10 years?
Solution: Distance in a year = 100 × 365 = 36,500 km. In 10 years = 36,500 × 10 = 3,65,000 km. Since 3,65,000 km < 3,84,400 km, no, you would not quite reach the Moon in 10 years — you’d fall about 19,400 km short.

Q (Reasonable assumptions). (a) A sheet of paper weighs about 5 g; could you lift 1 lakh sheets at once? (b) If 250 babies are born every minute worldwide, will a million be born in a single day? (c) At 1 coin/second, can you count 1 million coins in a day?
Solution: (a) 1,00,000 × 5g = 5,00,000 g = 500 kg — far too heavy to lift at once, so no. (b) Minutes in a day = 24×60 = 1,440; babies/day = 250×1,440 = 3,60,000, which is less than a million, so no. (c) Seconds in a day = 24×60×60 = 86,400; 10,00,000 ÷ 86,400 ≈ 11.6 days, so no, you cannot count 1 million coins in a single day.

Challenge Problems (Figure It Out)

Q. Using each digit 0–9 exactly once (first digit ≠ 0), form: (a) the largest 10-digit multiple of 5 (b) the smallest 10-digit even number.
Solution: (a) 9876543210 (digits in descending order, ending in 0 so it’s a multiple of 5). (b) 1023456798 (smallest possible leading digits in ascending order, with the last two digits swapped to make the final digit even).

Q. Find the only 9-digit number (using digits 1–9 exactly once) where swapping ANY two digits always increases its value.
Solution: 123456789 — since its digits are in strictly increasing order matching their place values, moving any larger digit to a more significant (leftward) position by a swap always increases the number’s value. This is the only such arrangement.

Q. From the 20-digit number 12345123451234512345, strike out 10 digits to leave the largest possible 10-digit number (keeping the remaining digits in their original order).
Solution: Using a greedy “keep the largest possible digit at each step while leaving enough digits for the rest” strategy: 5534512345.

Q. What is the 1000th digit when you write out 1,2,3,4,5,… consecutively? What number contains the millionth digit?
Solution: Digits 1–9 contribute 9 digits; digits 10–99 contribute 180 more (cumulative 189). The remaining 811 digits (up to 1000) fall among 3-digit numbers: 811÷3 = 270 complete numbers, reaching cumulative 999 at the end of the number 369. So the 1000th digit is the first digit of 370, which is 3. Using the same method for the millionth digit: cumulative digits through all 5-digit numbers = 4,88,889; the remaining 5,11,111 digits fall among 6-digit numbers, and 5,11,110÷6 = 85,185 complete numbers reach cumulative 999,999 at the end of 1,85,184 — so the millionth digit is the first digit of the number 1,85,185.

Q. A calculator has only “+10,000” and “+100” buttons. How many total presses to reach: (a) 20,800 (b) 92,100 (c) 1,20,500?
Solution: (a) 20,800 = 2×10,000 + 8×100 ⇒ 10 presses. (b) 92,100 = 9×10,000 + 21×100 ⇒ 30 presses. (c) 1,20,500 = 12×10,000 + 5×100 ⇒ 17 presses.

Q. How many lakhs make a billion?
Solution: 1 billion = 1,00,00,00,000; 1 lakh = 1,00,000. 1,00,00,00,000 ÷ 1,00,000 = 10,000 lakhs make a billion.

Q (Statue of Unity in coins). If coins are stacked 1 mm thick each, how many coins would match the Statue of Unity’s height of 180 m?
Solution: 180 m = 1,80,000 mm. At 1 mm/coin: 1,80,000 coins would be needed. (Note: some published answer keys give 1,82,000, but this doesn’t match the stated 1,80,000 mm height ÷ 1 mm/coin — the correct figure is 1,80,000.)

Q (Digit-counting challenge). When is the digit ‘5’ written for the 5000th time while writing out the counting numbers 1, 2, 3, …?
Solution: Using the standard digit-frequency counting method (tallying occurrences of ‘5’ separately by place value: units, tens, hundreds, and so on), the cumulative count of the digit 5 reaches exactly 5,000 at the units digit of the number 13,495. (Verified independently via the digit-position counting formula: occurrences of ‘5’ from 1 to 13,495 total exactly 1,350+1,350+1,300+1,000 = 5,000 across the units, tens, hundreds and thousands positions respectively; some other sources give 13,995 for this answer, but that figure doesn’t check out against a careful recount.)

Why This Chapter Matters (for Boards)

Fluency with the Indian numbering system (lakh, crore), the International system (million, billion), and comparing/estimating large numbers is essential groundwork for later topics in ratios, percentages, and real-world data interpretation across Class 7-10.

More on This Chapter

See also: Class 7 Maths Part 1 NCERT Book (Ganita Prakash) and the Class 7 Maths Formulas Handbook.

Related pages: Extra Questions for Class 7 Maths Chapter 1 | Revision Notes for Class 7 Maths Chapter 1

Frequently Asked Questions

Q: What’s the difference between the Indian and International numbering systems?
A: The Indian system groups digits as thousand, lakh, crore (using commas after 3, then every 2 digits: e.g. 1,23,45,678), while the International system groups every 3 digits as thousand, million, billion (e.g. 12,345,678).

Q: What’s a quick way to estimate a sum or difference before calculating exactly?
A: Round each number to its largest place value (nearest lakh, thousand, etc.), then add/subtract the rounded values — this gives a ballpark figure to sanity-check your exact calculation against.