Chapter 1 exercise answers: Large Numbers Around Us

Open NCERT p. 3Matches NCERT’s answer

1. One lakh is 1,00,000.
2. Subtract the population from one lakh: 1,00,000 − 75,000 = 25,000.

Answer25,000

Watch this explained “A town on either side of the line”, 3:13 into What it actually takes to make one lakh · हिंदी में देखें

Open NCERT p. 3Matches NCERT’s answer

1. One lakh is 1,00,000.
2. Subtract one lakh from the 2024 population: 1,06,000 − 1,00,000 = 6,000.

Answer6,000

Watch this explained “A town on either side of the line”, 3:13 into What it actually takes to make one lakh · हिंदी में देखें

Open NCERT p. 3Matches NCERT’s answer

1. The 2011 population was 75,000 and the 2024 population is 1,06,000.
2. Subtract: 1,06,000 − 75,000 = 31,000.

Answer31,000

Watch this explained “A town on either side of the line”, 3:13 into What it actually takes to make one lakh · हिंदी में देखें

Open NCERT p. 6Checked by computerAnswers can differ: one example

(a) 8300

1. Place-value way: (8×1000)+(3×100) = 8300.
2. Trade one 1000 for ten 100s: (7×1000)+(13×100) = 8300.

Answer8×1000 + 3×100, or 7×1000 + 13×100

(b) 40629

1. Place-value way: (4×10000)+(6×100)+(2×10)+(9×1) = 40629.
2. Trade one 10000 for ten 1000s: (3×10000)+(10×1000)+(6×100)+(2×10)+(9×1) = 40629.

Answer4×10000 + 6×100 + 2×10 + 9×1, or 3×10000 + 10×1000 + 6×100 + 2×10 + 9×1

(c) 56354

1. Place-value way: (5×10000)+(6×1000)+(3×100)+(5×10)+(4×1) = 56354.
2. Trade one 10000 for ten 1000s: (4×10000)+(16×1000)+(3×100)+(5×10)+(4×1) = 56354.

Answer5×10000 + 6×1000 + 3×100 + 5×10 + 4×1, or 4×10000 + 16×1000 + 3×100 + 5×10 + 4×1

(d) 66666

1. Place-value way: (6×10000)+(6×1000)+(6×100)+(6×10)+(6×1) = 66666.
2. Trade one 10000 for ten 1000s: (5×10000)+(16×1000)+(6×100)+(6×10)+(6×1) = 66666.

Answer6×10000 + 6×1000 + 6×100 + 6×10 + 6×1, or 5×10000 + 16×1000 + 6×100 + 6×10 + 6×1

(e) 367813

1. Place-value way: (3×100000)+(6×10000)+(7×1000)+(8×100)+(1×10)+(3×1) = 367813.
2. Trade one 100000 for ten 10000s: (2×100000)+(16×10000)+(7×1000)+(8×100)+(1×10)+(3×1) = 367813.

Answer3×100000 + 6×10000 + 7×1000 + 8×100 + 1×10 + 3×1, or 2×100000 + 16×10000 + 7×1000 + 8×100 + 1×10 + 3×1

Watch this explained “Seventy-two ways to make one number”, 3:00 into The Land of Tens: each place is ten of the one before · हिंदी में देखें

Open NCERT p. 7Checked by computerAnswers can differ: one example

1. Systematic Sippy has the buttons +1, +10, +100, +1000, +10000 and +1,00,000.
2. Ten presses of a button can always be replaced by one press of the next bigger button: the total stays the same and 9 clicks are saved. So the fewest clicks never press any button 10 or more times — each button is pressed as many times as the digit in its place.
3. 8300: (8 × 1000) + (3 × 100), that is 8 + 3 = 11 clicks.
4. 40629: (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1), that is 4 + 6 + 2 + 9 = 21 clicks.
5. 56354: (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1), that is 23 clicks.
6. 66666: (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1), that is 30 clicks.
7. 367813: (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1), that is 28 clicks.

Answer(a) 8 × 1000 + 3 × 100 (11 clicks); (b) 4 × 10000 + 6 × 100 + 2 × 10 + 9 × 1 (21 clicks); (c) 5 × 10000 + 6 × 1000 + 3 × 100 + 5 × 10 + 4 × 1 (23 clicks); (d) 6 × 10000 + 6 × 1000 + 6 × 100 + 6 × 10 + 6 × 1 (30 clicks); (e) 3 × 100000 + 6 × 10000 + 7 × 1000 + 8 × 100 + 1 × 10 + 3 × 1 (28 clicks)

Watch this explained “The fewest presses”, 4:38 into The Land of Tens: each place is ten of the one before · हिंदी में देखें

Open NCERT p. 7One way to think about it

1. From the previous question, the fewest clicks are: 8300 → 11, 40629 → 21, 56354 → 23, 66666 → 30, 367813 → 28.
2. Add the digits of each number: 8 + 3 + 0 + 0 = 11, 4 + 0 + 6 + 2 + 9 = 21, 5 + 6 + 3 + 5 + 4 = 23, 6 + 6 + 6 + 6 + 6 = 30, 3 + 6 + 7 + 8 + 1 + 3 = 28.
3. They match every time, because in the fewest-click way each button is pressed as many times as the digit in its place.

In shortYes — the smallest number of button clicks equals the sum of the digits of the number. For example, 8300 needs 8 + 3 = 11 clicks. (This works because Sippy has a button for every place of these numbers.)

Watch this explained “The cheapest recipe IS the number”, 6:10 into The Land of Tens: each place is ten of the one before · हिंदी में देखें

Open NCERT p. 7One way to think about it

1. Suppose some way of making a number presses one button 10 or more times.
2. Ten presses of that button add the same amount as one press of the next bigger button (for example, ten presses of +100 add 1000). Swapping them keeps the number the same and saves 9 clicks.
3. So the way with the fewest clicks never presses any button 10 or more times — each button is pressed 0 to 9 times.
4. Writing each button's count in its own place, from the biggest button to +1, gives a list of single digits. That is exactly how the number is written in place value notation, so the fewest-click expression and the place value notation are the same thing.

In shortBecause pressing any button ten times can always be replaced by one press of the next bigger button, saving 9 clicks. So the fewest-click way presses each button only 0 to 9 times — one digit per place — which is exactly the number's place value notation. (This needs a button for every place, which Sippy has for these numbers.)

Watch this explained “Trade down, pay nine”, 5:21 into The Land of Tens: each place is ten of the one before · हिंदी में देखें

Open NCERT p. 9Matches NCERT’s answer

(a) 4050678

1. Indian commas: 40,50,678 → 40 lakh, 50 thousand, 678.
2. American commas: 4,050,678 → 4 million, 50 thousand, 678.

AnswerIndian: forty lakh fifty thousand six hundred seventy-eight. American: four million fifty thousand six hundred seventy-eight.

(b) 48121620

1. Indian commas: 4,81,21,620 → 4 crore, 81 lakh, 21 thousand, 620.
2. American commas: 48,121,620 → 48 million, 121 thousand, 620.

AnswerIndian: four crore eighty-one lakh twenty-one thousand six hundred twenty. American: forty-eight million one hundred twenty-one thousand six hundred twenty.

(c) 20022002

1. Indian commas: 2,00,22,002 → 2 crore, 00 lakh, 22 thousand, 2 (the lakh group is 00, so it is not said).
2. American commas: 20,022,002 → 20 million, 22 thousand, 2.

AnswerIndian: two crore twenty-two thousand two. American: twenty million twenty-two thousand two.

(d) 246813579

1. Indian commas: 24,68,13,579 → 24 crore, 68 lakh, 13 thousand, 579.
2. American commas: 246,813,579 → 246 million, 813 thousand, 579.

AnswerIndian: 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) 345000543

1. Indian commas: 34,50,00,543 → 34 crore, 50 lakh, 00 thousand, 543.
2. American commas: 345,000,543 → 345 million, 000 thousand, 543.

AnswerIndian: thirty-four crore fifty lakh five hundred forty-three. American: three hundred forty-five million five hundred forty-three.

(f) 1020304050

1. Indian commas: 1,02,03,04,050 → 1 arab, 02 crore, 03 lakh, 04 thousand, 050.
2. American commas: 1,020,304,050 → 1 billion, 020 million, 304 thousand, 050.

AnswerIndian: one arab two crore three lakh four thousand fifty (or one hundred two crore three lakh four thousand fifty). American: one billion twenty million three hundred four thousand fifty.

Watch this explained “A ten-digit number read aloud, twice”, 4:34 into Crores and millions: one number, two naming systems · हिंदी में देखें

Open NCERT p. 9Matches NCERT’s answer

(a) One crore one lakh one thousand ten

1. 1 crore = 1,00,00,000; 1 lakh = 1,00,000; 1 thousand = 1,000; ten = 10.
2. Add: 1,00,00,000 + 1,00,000 + 1,000 + 10 = 1,01,01,010.

Answer1,01,01,010

(b) One billion one million one thousand one

1. 1 billion = 1,00,00,00,000 (1 arab); 1 million = 10,00,000 (10 lakh); 1 thousand = 1,000; one = 1.
2. Add: 1,00,00,00,000 + 10,00,000 + 1,000 + 1 = 1,00,10,01,001.

Answer1,00,10,01,001

(c) Ten crore twenty lakh thirty thousand forty

1. 10 crore = 10,00,00,000; 20 lakh = 20,00,000; 30 thousand = 30,000; forty = 40.
2. Add: 10,00,00,000 + 20,00,000 + 30,000 + 40 = 10,20,30,040.

Answer10,20,30,040

(d) Nine billion eighty million seven hundred thousand six hundred

1. 9 billion = 9,00,00,00,000 (9 arab); 80 million = 8,00,00,000 (8 crore); 7 hundred thousand = 7,00,000 (7 lakh); six hundred = 600.
2. Add: 9,00,00,00,000 + 8,00,00,000 + 7,00,000 + 600 = 9,08,07,00,600.

Answer9,08,07,00,600

Watch this explained “Seven quantities, each named twice”, 2:11 into Crores and millions: one number, two naming systems · हिंदी में देखें

Open NCERT p. 9Matches NCERT’s answer

(a) 30 thousand ____ 3 lakhs

1. 30 thousand = 30,000; 3 lakhs = 3,00,000.
2. 30,000 is less than 3,00,000.

Answer<

(b) 500 lakhs ____ 5 million

1. 500 lakhs = 5,00,00,000; 5 million = 50,00,000.
2. 5,00,00,000 is more than 50,00,000.

Answer>

(c) 800 thousand ____ 8 million

1. 800 thousand = 8,00,000; 8 million = 80,00,000.
2. 8,00,000 is less than 80,00,000.

Answer<

(d) 640 crore ____ 60 billion

1. 640 crore = 6,40,00,00,000; 60 billion = 60,00,00,00,000.
2. 6.4 billion is less than 60 billion.

Answer<

Watch this explained “Convert first, then compare”, 6:26 into Crores and millions: one number, two naming systems · हिंदी में देखें

Open NCERT p. 14Matches NCERT’s answer

(a) 2 × 1768 × 50

1. Reorder: 2 × 50 = 100 first.
2. 100 × 1768 = 176800.

Answer176800

(b) 72 × 125

1. 125 = 1000/8, so 72 × 125 = 72 × 1000 / 8.
2. 72/8 = 9, then 9 × 1000 = 9000.

Answer9000

(c) 125 × 40 × 8 × 25

1. Pair up: 125 × 8 = 1000, and 40 × 25 = 1000.
2. 1000 × 1000 = 1,000,000.

Answer1,000,000

Watch this explained “Both freedoms at once — 125 x 40 x 8 x 25”, 5:24 into Factorise and regroup instead of multiplying head-on · हिंदी में देखें

Open NCERT p. 14Checked by computerAnswers can differ: one example

(a) 25 × 12 =

1. 25 × 12 = 300.

Answer300

(b) 25 × 240 =

1. 240 is 12 × 20, so 25 × 240 = (25 × 12) × 20 = 300 × 20 = 6000.

Answer6000

(c) 250 × 120 =

1. 250 is 25 × 10 and 120 is 12 × 10, so the product is 300 × 100 = 30000.

Answer30000

(d) 2500 × 12 =

1. 2500 is 25 × 100, so 2500 × 12 = 300 × 100 = 30000.

Answer30000

(e) ___ × ___ = 120000000

1. Continue the same scaling pattern: 12000 × 10000 = 120,000,000.

Answer12000 × 10000 (one valid pair among several)

Watch this explained “The same idea one size up — 824 x 25”, 1:43 into Factorise and regroup instead of multiplying head-on · हिंदी में देखें

Open NCERT p. 19Matches NCERT’s answer

(a) Largest multiple of 5

1. The largest 10-digit number using each digit 0–9 once has the digits in decreasing order: 9876543210.
2. It ends in 0, so it is a multiple of 5. Nothing larger can be made, so this is the answer.

Answer9876543210

(b) Smallest even number

1. To make the number small, the first places must hold the smallest digits allowed: 1 first (0 cannot come first), then 0, 2, 3, 4, 5, 6, 7.
2. Only 8 and 9 are left for the last two places. An even number must end in an even digit, so the 8 goes last: …98.
3. So the smallest even number is 1023456798.

Answer1023456798

Open NCERT p. 20Checked by computerAnswers can differ: one example

1. Count letters the way the book does: 'Ten lakhs thirty thousand two hundred eighty five' has 3 + 5 + 6 + 8 + 3 + 7 + 6 + 4 = 42 letters (no 'and', spaces not counted).
2. A 7-digit name has three parts: the lakhs (10 to 99), the thousands (0 to 99) and the last three digits (0 to 999). Each part can be made as long as possible on its own.
3. The longest name for a number from 10 to 99 has 12 letters: seventy three, seventy seven or seventy eight ('seventy' is the longest tens word; 'three', 'seven' and 'eight' are the longest units words).
4. The longest name for a number from 0 to 999 has 24 letters, such as seven hundred seventy seven.
5. So the most letters possible is (12 + 5 for 'lakhs') + (12 + 8 for 'thousand') + 24 = 61.
6. 77,77,777 is seventy seven lakhs seventy seven thousand seven hundred seventy seven: 7 + 5 + 5 + 7 + 5 + 8 + 5 + 7 + 7 + 5 = 61 letters.

Answer77,77,777 — seventy seven lakhs seventy seven thousand seven hundred seventy seven, with 61 letters. Other answers are possible: 81 different numbers reach 61 letters, such as 73,73,373 and 78,78,878.

Watch this explained “Where the comma goes”, 7:39 into What it actually takes to make one lakh · हिंदी में देखें

Open NCERT p. 20Checked by computer

1. If two digits are the same, exchanging them gives the same number, not a bigger one. So all 9 digits must be different.
2. If some digit is bigger than the digit just after it, exchanging those two puts the smaller digit in the higher place and the number gets smaller. So every digit must be smaller than the one after it: the digits increase from left to right.
3. Increasing digits do work: any exchange then moves a bigger digit into a higher place, so the number always gets bigger.
4. Nine different digits leave out one of 0–9. If 0 were used, increasing order would put it first, which is not allowed, so 0 is the digit left out.
5. That leaves only 1, 2, 3, …, 9 in increasing order: 123456789.
6. The answer key at the back of the book prints 987654312, but swapping its first two digits gives 897654312, which is smaller; only 123456789 gets bigger whichever two digits you swap, so it is the one such number.

Answer123456789. Only 1 such number exists.

Open NCERT p. 20Matches NCERT’s answer

1. 20 digits minus the 10 struck out leaves 10 digits, still in their order. To make the number as large as possible, make the first kept digit as large as possible, then the second, and so on.
2. The first kept digit must leave 9 digits after it, so it comes from the first 11 digits (1 2 3 4 5 1 2 3 4 5 1). The largest is the first 5, so strike out the 1, 2, 3, 4 before it.
3. The second kept digit must leave 8 after it, so it comes from places 6 to 12 (1 2 3 4 5 1 2). The largest is the 5 in place 10, so strike out 1, 2, 3, 4.
4. The third kept digit must leave 7 after it, so it comes from places 11 to 13 (1 2 3). The largest is 3, so strike out 1, 2.
5. That is 4 + 4 + 2 = 10 digits struck out, and the last 7 digits, 4512345, all stay.

Answer5534512345

Open NCERT p. 20Checked by computer

1. Start counting: every pair shares a letter — zero/one (e, o), four/five (f), nine/ten (n, e), nineteen/twenty (n, e, t), ninety nine/one hundred (n, e). A computer check of every pair up to one crore, naming numbers in both the Indian and the American way, finds no pair without a common letter.
2. For bigger numbers there is a reason. Two neighbours with the same number of digits (3 or more) both contain the same big word — hundred, thousand, lakh, crore, million, and so on — so they share its letters.
3. The only other kind of neighbours is like 999 and 1000, where the number of digits goes up. The smaller one ends in 'nine' and the larger one begins with 'one' or 'ten' (one thousand, ten thousand, one lakh, ten lakh, one crore…). Both contain the letters n and e.
4. So two consecutive numbers always share at least one letter.

AnswerYou never find such a pair: however far you count, two consecutive numbers always share at least one English letter.

Open NCERT p. 20Checked by computer

(a) What would the 1000th digit be? At which number would it occur?

1. 1 to 9: 9 numbers × 1 digit = 9 digits. 10 to 99: 90 numbers × 2 digits = 180 digits. Together 189 digits.
2. Numbers from 100 to 999 use 3 digits each. The 1000th digit is 1000 − 189 = 811 digits into this part.
3. 811 = 270 × 3 + 1, so 270 three-digit numbers (100 to 369) come first, and the 1000th digit is the 1st digit of the next number, 370.
4. The 1st digit of 370 is 3.

AnswerThe 1000th digit is 3, in the number 370.

(b) What number would contain the millionth digit?

1. Digits used: 1–9 → 9; 10–99 → 180; 100–999 → 2,700; 1000–9999 → 36,000; 10000–99999 → 4,50,000. Total 4,88,889.
2. The millionth digit is 10,00,000 − 4,88,889 = 5,11,111 digits into the 6-digit numbers.
3. 5,11,111 = 85,185 × 6 + 1, so 85,185 six-digit numbers (1,00,000 to 1,85,184) come first, and the millionth digit is the 1st digit of 1,85,185.

Answer1,85,185

(c) When would you have written the digit '5' for the 5000th time?

1. From 1 to 9,999 the digit 5 appears 1,000 times in each of the units, tens, hundreds and thousands places: 4,000 fives.
2. From 10,000 to 12,999 the first two digits (10, 11, 12) have no 5, and the last three places give 300 fives in each thousand: 900 more, 4,900 in all.
3. From 13,000 to 13,499 the hundreds digit is 0 to 4, so only the tens and units give 5s: 50 + 50 = 100 more, reaching 5,000.
4. The last 5 written in that stretch is the units digit of 13,495 (13,496 to 13,499 have no 5).
5. The answer key at the back of the book prints 13995, but by then the digit 5 has already been written 5200 times; the 5000th 5 is the last digit of 13495, so the answer is 13495.

AnswerWhile writing 13,495.

Open NCERT p. 20Checked by computerAnswers can differ: one example

(a) 20,800

1. Any mix of the two buttons that adds up to the number is a correct expression; the ones here use the fewest clicks, by pressing +10,000 as many times as it fits.
2. 2 × 10,000 = 20,000, leaving 800 = 8 × 100.

Answer2 × 10,000 + 8 × 100 (10 clicks)

(b) 92,100

1. 9 × 10,000 = 90,000, leaving 2,100 = 21 × 100.

Answer9 × 10,000 + 21 × 100 (30 clicks)

(c) 1,20,500

1. 12 × 10,000 = 1,20,000, leaving 500 = 5 × 100.

Answer12 × 10,000 + 5 × 100 (17 clicks)

(d) 65,30,000

1. 65,30,000 ÷ 10,000 = 653, with nothing left over.

Answer653 × 10,000 (653 clicks)

(e) 70,25,700

1. 702 × 10,000 = 70,20,000, leaving 5,700 = 57 × 100.

Answer702 × 10,000 + 57 × 100 (759 clicks)

Watch this explained “When the rule breaks”, 7:02 into The Land of Tens: each place is ten of the one before · हिंदी में देखें

Open NCERT p. 20Matches NCERT’s answer

1. A billion is 1 followed by 9 zeros; a lakh is 1 followed by 5 zeros.
2. Divide: a billion ÷ a lakh = 10^9 ÷ 10^5 = 10^4 = 10,000.

Answer10,000 lakhs make a billion.

Watch this explained “Counting the zeros: 5, 6, 7, 9”, 3:00 into Crores and millions: one number, two naming systems · हिंदी में देखें

Open NCERT p. 20Checked by computerReads two ways: both answers shown

(a) largest possible sum

1. There are 7 boxes in the top row and 5 in the bottom row, so we make a 7-digit number and a 5-digit number.
2. The book does not say which cards may go in which row, so there are two ways to read it. Reading 1 (what the words say): all 18 cards are shared, so a digit can appear twice in the same number. Reading 2 (what the two box colours suggest): one set of cards 1 – 9 for each number, so no digit repeats inside a number.
3. For the largest sum, put the biggest digits in the biggest places. The top number's first two places (ten lakhs and lakhs) are bigger than anything in the bottom number, so they get the biggest digits.
4. Reading 1: the two 9s go in the top number's first two places. The two 8s go in the ten thousands places of both numbers, the two 7s in the thousands places, and so on. Top: 99,87,654. Bottom: 87,654.
5. 99,87,654 + 87,654 = 1,00,75,308.
6. Reading 2: each number uses its own set, largest digits first. Top: 98,76,543. Bottom: 98,765.
7. 98,76,543 + 98,765 = 99,75,308.

AnswerReading 1, all 18 cards shared: 99,87,654 + 87,654 = 1,00,75,308. Reading 2, one set for each number: 98,76,543 + 98,765 = 99,75,308.

(b) smallest possible difference

1. A 7-digit number is always bigger than a 5-digit number, so the difference is top number − bottom number.
2. To make the difference as small as possible, make the top number as small as possible and the bottom number as large as possible.
3. Reading 1 (all 18 cards shared): smallest top number 11,22,334 (using both 1s, both 2s, both 3s and a 4). Largest bottom number from the cards left: 99,887.
4. 11,22,334 − 99,887 = 10,22,447.
5. Reading 2 (one set for each number): smallest top number 12,34,567. Largest bottom number 98,765.
6. 12,34,567 − 98,765 = 11,35,802.

AnswerReading 1, all 18 cards shared: 11,22,334 − 99,887 = 10,22,447. Reading 2, one set for each number: 12,34,567 − 98,765 = 11,35,802.

Open NCERT p. 21Checked by computer

(b) 2,00,000:

1. This is a challenge, so any correct way of reaching these numbers is fine; here is one for each.
2. 70000 × 5 = 3,50,000.
3. 3,50,000 − 1,50,000 = 2,00,000.

Answer70000 × 5 − 150000 = 2,00,000 (exact)

(c) 5,80,000:

1. 4000 × 20 = 80,000 and 70000 × 5 = 3,50,000.
2. 1,50,000 + 80,000 + 3,50,000 = 5,80,000.

Answer150000 + 4000 × 20 + 70000 × 5 = 5,80,000 (exact)

(d) 12,45,000:

1. 13000 + 70000 = 83,000 and 20 − 5 = 15.
2. 83,000 × 15 = 12,45,000.

Answer(13000 + 70000) × (20 − 5) = 12,45,000 (exact)

(e) 20,90,800:

1. 150000 − 13000 = 1,37,000, and 1,37,000 ÷ 20 = 6,850.
2. 300 − 5 = 295, and 6,850 × 295 = 20,20,750.
3. 20,20,750 + 70000 = 20,90,750, which is 50 less than 20,90,800.
4. A computer search of every way to combine the cards with +, −, × and ÷, with every step giving a whole number, finds nothing closer.
5. The answer key at the back of the book prints 12,44,500 and 20,91,000, but 300 × (13000 + 70000) ÷ 20 makes 12,45,000 exactly, and the key's 20,91,000 multiplies by 14, which is not a card, while 70000 + (150000 − 13000) ÷ 20 × (300 − 5) = 20,90,750 is only 50 away.

Answer70000 + (150000 − 13000) ÷ 20 × (300 − 5) = 20,90,750 (50 short of 20,90,800; the closest possible when every step is a whole number)

Open NCERT p. 21Matches NCERT’s answer

1. The Statue of Unity is about 180 metres tall (given earlier in the chapter).
2. Convert to millimetres: 180 × 1000 = 1,80,000 mm.
3. Since each coin is 1 mm thick, that many coins are needed.

Answer1,80,000 coins

Watch this explained “Birds, coins and mountains — the method turned loose”, 8:44 into Answering "could this possibly fit?" by estimating in stages · हिंदी में देखें

Open NCERT p. 21Checked by computerReads two ways: both answers shown

1. The trip is about 12,000 km. The bird covers 900 to 1000 km in a day.
2. Flying fast (1000 km a day): 12,000 ÷ 1000 = 12 days.
3. Flying slower (900 km a day): 12,000 ÷ 900 = 40/3 = 13 1/3 days.
4. So the trip takes from 12 days to 13 1/3 days.
5. Counting in whole days, 13 1/3 days means the bird is still flying on the 14th day. NCERT's answer key uses this reading: about 12 to 14 days.

AnswerAbout 12 to 14 days, counting whole days (NCERT's answer key). Exactly, it is 12 days to 40/3 = 13 1/3 days.

Watch this explained “Birds, coins and mountains — the method turned loose”, 8:44 into Answering "could this possibly fit?" by estimating in stages · हिंदी में देखें

Open NCERT p. 21Checked by computer

1. Distance in one day = 13,560 km ÷ 11 days = 1232.72… km, which is about 1233 km.
2. One day has 24 hours, so 11 days have 11 × 24 = 264 hours.
3. Distance in one hour = 13,560 km ÷ 264 hours = 51.36… km, which is about 51 km.
4. Dividing the rounded figure also works: 1233 ÷ 24 = 51.3…, again about 51 km. This is how NCERT's answer key does it.

AnswerAbout 1233 km every day and about 51 km every hour (exactly 13560/11 km a day and 565/11 km an hour).

Watch this explained “Birds, coins and mountains — the method turned loose”, 8:44 into Answering "could this possibly fit?" by estimating in stages · हिंदी में देखें

Open NCERT p. 21Checked by computer

1. First find the height of Somu's building (page 3). Somu is 1 m tall and each floor is about 4 times his height, so one floor is about 4 m.
2. The building has 10 floors with balconies, so it is about 10 × 4 = 40 m tall. NCERT's answer key uses 40 m.
3. Bald eagles: 4500 ÷ 40 = 112.5 and 6000 ÷ 40 = 150. So they fly about 112.5 to 150 times the height of the building. (NCERT's key rounds 112.5 and writes 'about 112 to 150'.)
4. Mount Everest: 8850 ÷ 40 = 221.25, so it is about 221 times as tall.
5. Aeroplanes: 10,000 ÷ 40 = 250 and 12,800 ÷ 40 = 320. So they fly about 250 to 320 times as high.
6. These are estimates. If you also count the short ground floor with the door, the building is about 44 m and every answer is a little smaller (Everest about 201 times).

AnswerWith the building about 40 m tall: bald eagles 112.5 to 150 times; Mount Everest 221.25, about 221 times; aeroplanes 250 to 320 times.

Watch this explained “Birds, coins and mountains — the method turned loose”, 8:44 into Answering "could this possibly fit?" by estimating in stages · हिंदी में देखें