NCERT Solutions Class 7 Maths Part 1 Chapter 1 Large Numbers Around Us PDF

1. One lakh means 1,00,000.
2. 1,00,000 - 75,000 = 25,000, so 75,000 is 25,000 less than one lakh.
3. 1,06,000 - 1,00,000 = 6,000, so 1,06,000 is 6,000 more than one lakh.
4. 1,06,000 - 75,000 = 31,000, so the population increased by 31,000.

Answer: 25,000 less, 6,000 more, and an increase of 31,000.

1. The largest 3-digit number is 999.
2. Adding 1 gives 1000, the smallest 4-digit number.
3. The largest 4-digit number is 9999.
4. Adding 1 gives 10,000, the smallest 5-digit number.
5. The largest 5-digit number is 99,999.
6. Adding 1 gives 1,00,000, the smallest 6-digit number, read as one lakh.

Answer: 999, 1000, 9999, 10,000, 99,999, 1,00,000.

1. Days in 100 years = 365 x 100 = 36,500.
2. At 1 variety each day: 36,500 varieties.
3. At 2 varieties each day: 73,000 varieties.
4. At 3 varieties each day: 1,09,500 varieties.
5. Only 3 varieties per day crosses one lakh.

Answer: One and two per day are not enough. Three per day is enough.

1. Each floor is about 4 m.
2. The picture shows a 10-floor building, so its height is about 10 x 4 = 40 m.
3. The Statue of Unity is about 180 m. It is taller by 180 - 40 = 140 m.
4. Kunchikal waterfall is about 450 m. It is taller by 450 - 40 = 410 m.
5. Floors needed for a 450 m height = 450 / 4 = 112.5, so about 113 floors.

Answer: Building about 40 m, statue 140 m taller, waterfall 410 m taller, about 113 floors.

1. 3,00,600 is three lakh six hundred.
2. 5,04,085 is five lakh four thousand eighty five.
3. 27,30,000 is twenty seven lakh thirty thousand.
4. 70,53,138 is seventy lakh fifty three thousand one hundred thirty eight.

Answer: Three lakh six hundred; five lakh four thousand eighty five; twenty seven lakh thirty thousand; seventy lakh fifty three thousand one hundred thirty eight.

1. One lakh twenty three thousand four hundred fifty six = 1,23,456.
2. Four lakh seven thousand seven hundred four = 4,07,704.
3. Fifty lakhs five thousand fifty = 50,05,050.
4. Ten lakhs two hundred thirty five = 10,00,235.

Answer: 1,23,456; 4,07,704; 50,05,050; 10,00,235.

1. +1000 calculator: 10,000 needs 10 presses, 53,000 needs 53, 90,000 needs 90, 1,00,000 needs 100, and 153 presses gives 1,53,000.
2. +10 calculator: 500 needs 50 presses, 780 needs 78, 1000 needs 100, 3700 needs 370, 10,000 needs 1000, 1,00,000 needs 10,000, and 435 presses gives 4350.
3. +100 calculator: 400 needs 4 presses, 3700 needs 37, 10,000 needs 100, 53,000 needs 530, 90,000 needs 900, 97,600 needs 976, 1,00,000 needs 1000, and 582 presses gives 58,200.
4. The +100 calculator can show multiples of 100. The +10 calculator can show all multiples of 10, so it can show every multiple of 100 too. The statement that Handy Hundreds can show a number Tedious Tens cannot is false.

Answer: Use target number divided by button value. Handy Hundreds has no extra multiples beyond Tedious Tens.

1. 8300 = 8 x 1000 + 3 x 100 = 83 x 100.
2. 40629 = 4 x 10000 + 6 x 100 + 2 x 10 + 9 = 40 x 1000 + 62 x 10 + 9.
3. 56354 = 5 x 10000 + 6 x 1000 + 3 x 100 + 5 x 10 + 4 = 56 x 1000 + 354.
4. 66666 = 6 x 10000 + 6 x 1000 + 6 x 100 + 6 x 10 + 6 = 66 x 1000 + 666.
5. 367813 = 3 x 100000 + 6 x 10000 + 7 x 1000 + 8 x 100 + 1 x 10 + 3 = 367 x 1000 + 813.

Answer: Each number can be split by place value or by regrouped place values.

1. Use the place-value digits as button counts.
2. 5072 = 5 x 1000 + 7 x 10 + 2, so 14 clicks.
3. 8300 = 8 x 1000 + 3 x 100, so 11 clicks.
4. 40629 = 4 x 10000 + 6 x 100 + 2 x 10 + 9, so 21 clicks.
5. 56354 = 5 + 6 + 3 + 5 + 4 = 23 clicks by place values.
6. 66666 = 6 + 6 + 6 + 6 + 6 = 30 clicks.
7. 367813 = 3 + 6 + 7 + 8 + 1 + 3 = 28 clicks.

Answer: 14, 11, 21, 23, 30, and 28 clicks.

1. 40,50,678: forty lakh fifty thousand six hundred seventy eight. American: four million fifty thousand six hundred seventy eight.
2. 4,81,21,620: four crore eighty one lakh twenty one thousand six hundred twenty. American: forty eight million one hundred twenty one thousand six hundred twenty.
3. 2,00,22,002: two crore twenty two thousand two. American: twenty million twenty two thousand two.
4. 24,68,13,579: 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.
5. 34,50,00,543: thirty four crore fifty lakh five hundred forty three. American: three hundred forty five million five hundred forty three.
6. 1,02,03,04,050: one arab two crore three lakh four thousand fifty. American: one billion twenty million three hundred four thousand fifty.

Answer: Use Indian groups 3,2,2,... and American groups 3,3,3,... from the right.

1. One crore one lakh one thousand ten = 1,01,01,010.
2. One billion one million one thousand one = 1,001,001,001.
3. Ten crore twenty lakh thirty thousand forty = 10,20,30,040.
4. Nine billion eighty million seven hundred thousand six hundred = 9,080,700,600.
5. 30 thousand < 3 lakhs, because 30,000 < 3,00,000.
6. 500 lakhs = 5 million, because both are 5,00,00,000? Wait: 500 lakhs = 5 crore = 50 million, so 500 lakhs > 5 million.
7. 800 thousand < 8 million, because 8,00,000 < 80,00,000.
8. 640 crore > 60 billion? Since 640 crore = 6.4 billion, it is less than 60 billion.

Answer: 1,01,01,010; 1,001,001,001; 10,20,30,040; 9,080,700,600; <, >, <, <.

1. For 3,87,69,957: nearest thousand 3,87,70,000; ten thousand 3,87,70,000; lakh 3,88,00,000; ten lakh 3,90,00,000; crore 4,00,00,000.
2. For 29,05,32,481: nearest thousand 29,05,32,000; ten thousand 29,05,30,000; lakh 29,05,00,000; ten lakh 29,10,00,000; crore 29,00,00,000.
3. For all five rounded values to be 5,00,00,000, the number must round to 5 crore even at the nearest thousand.
4. That gives numbers from 4,99,99,500 to 5,00,00,499, assuming usual rounding to nearest thousand.

Answer: The two neighbour lists are as above. There are 1000 such whole numbers under usual nearest-thousand rounding.

1. 4,63,128 + 4,19,682 = 8,82,810.
2. It is more than 8,00,000 and less than 9,00,000. Estu's estimate is closer.
3. 8,82,810 is greater than 8,50,000, and less than 8,83,128.
4. 14,63,128 - 4,90,020 = 9,73,108.
5. It is less than 10,00,000 and more than 9,00,000. Roxie's estimate is closer.
6. 9,73,108 is greater than 9,50,000 and greater than 9,63,128.

Answer: 8,82,810 and 9,73,108 with the comparisons listed above.

1. Most listed cities grew from 2001 to 2011. Kolkata is one exception.
2. A suitable title is Population of Some Indian Cities in 2001 and 2011.
3. Pune's 2011 population is 31,15,431. Its increase is 31,15,431 - 25,38,473 = 5,76,958, about 6 lakh.
4. Bengaluru increased by 84,25,970 - 43,01,326 = 41,24,644, the largest increase.
5. Bengaluru, Hyderabad, Surat, and Vadodara almost doubled.
6. Mumbai divided by Patna is about 1,24,42,373 / 16,84,222 = 7.39, so multiply Patna by about 7.4.

Answer: Title, Pune increase, Bengaluru, the near-doubling cities, and multiplier about 7.4.

1. 2 x 50 = 100, so 2 x 1768 x 50 = 1,76,800.
2. 125 = 1000 / 8, so 72 x 125 = 9 x 1000 = 9000.
3. 125 x 8 = 1000 and 40 x 25 = 1000, so the product is 10,00,000.
4. 25 x 12 = 300; 25 x 240 = 6000; 250 x 120 = 30,000; 2500 x 12 = 30,000.
5. One possible product is 1200 x 1,00,000 = 120000000.

Answer: 1,76,800; 9000; 10,00,000; 300; 6000; 30,000; 30,000; for example 1200 x 1,00,000.

1. The product of an m-digit number and an n-digit number has either m+n-1 digits or m+n digits.
2. A 2-digit x 2-digit product is 3-digit or 4-digit, so Roxie is correct.
3. We need not try all cases. Check the smallest and largest possible products.
4. 3-digit x 3-digit cannot give a 4-digit product because 100 x 100 = 10,000.
5. 4-digit x 2-digit can give a 5-digit product, for example 1000 x 10 = 10,000.
6. 5-digit x 5-digit gives 9 or 10 digits. 8-digit x 3-digit gives 10 or 11 digits. 12-digit x 13-digit gives 24 or 25 digits.

Answer: The digit counts follow m+n-1 or m+n.

1. 1250 x 380 = 4,75,000. 2100 x 70,000 = 14,70,00,000. 6400 x 62,500 = 40,00,00,000.
2. 13,95,000 / 150 = 9300. 10,50,00,000 / 700 = 1,50,000. 52,00,00,00,000 / 130 = 4,00,00,000.
3. At 1000 km per day, reaching about 14,70,00,000 km takes 1,47,000 days, about 403 years. That is not a normal lifetime.
4. One lakh sheets at 5 g each weigh 5,00,000 g = 500 kg, too heavy to lift.
5. 250 babies per minute for 1440 minutes gives 3,60,000 babies, not one million.
6. At one coin per second, one day gives 86,400 coins, not one million.

Answer: The calculations support all the conclusions above.

1. A multiple of 5 must end in 0 or 5. To make the largest number, put 0 at the end and arrange the rest in descending order.
2. Largest multiple of 5 = 9876543210.
3. For the smallest even number, the first digit cannot be 0. Start with 1, then 0, then arrange remaining digits as small as possible while ending with an even digit.
4. A smallest valid even number is 1023456798.

Answer: 9876543210 and 1023456798.

1. One good 7-digit example is 77,77,777.
2. Its Indian name is seventy seven lakh seventy seven thousand seven hundred seventy seven, which is long.
3. For the 9-digit number, digits in descending order are already largest. We need one small inversion near the end.
4. 987654312 works because exchanging 1 and 2 gives 987654321, which is bigger.

Answer: 77,77,777 and 987654312 are valid examples.

1. We must keep 10 digits in the same order.
2. Choose the leftmost largest possible digit at each step while leaving enough digits to complete the answer.
3. The greedy selection gives 5534512345.
4. The two 5s come as early as possible, and then the largest remaining suffix is kept.

Answer: 5534512345.

1. Digits from 1 to 9 give 9 digits. Digits from 10 to 99 give 90 x 2 = 180 digits. Total to 99 is 189.
2. 1000 - 189 = 811 digits into the 3-digit numbers. 811 = 270 x 3 + 1, so the next number is 370 and the digit is 3.
3. For the millionth digit, counting by ranges places it in the number 1,85,185.
4. Counting occurrences of digit 5 gives the 5000th 5 at 13,995.

Answer: 1000th digit is 3 in 370; millionth digit is in 1,85,185; the 5000th 5 appears at 13,995.

1. 20,800 = 2 x 10,000 + 8 x 100, so 10 clicks.
2. 92,100 = 9 x 10,000 + 21 x 100, so 30 clicks.
3. 1,20,500 = 12 x 10,000 + 5 x 100, so 17 clicks.
4. 65,30,000 = 653 x 10,000, so 653 clicks.
5. 70,25,700 = 702 x 10,000 + 57 x 100, so 759 clicks.

Answer: The expressions and click counts are 10, 30, 17, 653, and 759 clicks.

1. One billion = 1,000,000,000. One lakh = 100,000. So a billion has 10,000 lakhs.
2. One largest-sum arrangement is 9988776 + 65544 = 1,00,54,320.
3. One smallest-difference arrangement is 1122334 - 99887 = 10,22,447.
4. For cards 4000, 13000, 300, 70000, 150000, 20, 5: 2,00,000 = 1,50,000 + 70,000 - 4000 x 5.
5. 5,80,000 = 1,50,000 x 4 - 4000 x 5. 12,44,500 is close to 12,45,000 using 70,000 x 20 - 1,50,000 - 4000 - 300 x 5.
6. 20,91,000 is close to 20,90,800 using 1,50,000 x 14 + 4000 - 13,000.

Answer: 10,000 lakhs, plus the card examples above.

1. Statue of Unity height = 180 m = 1,80,000 mm. At 1 mm per coin, use 1,80,000 coins.
2. A 12,000 km trip at 900 to 1000 km per day takes about 12 to 14 days.
3. The godwit covered 13,560 km in about 11 days. Per day: 13,560 / 11 = about 1233 km. Per hour: 1233 / 24 = about 51 km.
4. Somu's building is about 40 m. Bald eagle height 4500 to 6000 m is about 112.5 to 150 times.
5. Mount Everest: 8850 / 40 = about 221 times. Aeroplane height 10,000 to 12,800 m is about 250 to 320 times.

Answer: 1,80,000 coins; 12 to 14 days; about 1233 km/day and 51 km/hour; height ratios as listed.