NCERT Solutions Class 6 MathsChapter  1: Knowing our NumbersExercise 1.11. Fill in the blanks:(a) 1 lakh = Ten Ten thousand. Explanation: 1000 (3 Zeroes)  One Thousand Multiply by ten we get: 10000 (4 Zeroes)  Ten Thousand Multiply by ten we get: 100000 = Ten Ten Thousand or 1 Lakh (b) 1 million = Ten hundred thousand. Explanation: 100000 ( 5 Zeroes) 1 lakh or ten ten thousand or hundred thousand Multiply by ten we get: 1000000  1 million or Ten hundred thousand or Ten Lakh (c) 1 crore = Ten ten lakh. Explanation: 1000000 (6 Zeroes)  one million or ten lakh Multiply by ten we get: 10000000 (7 Zeroes)  1 crore (d) 1 crore = Ten million. Explanation: 1000000 (6 Zeroes)  one million or ten lakh 10000000 (7 Zeroes)  1 crore When we multiply Ten to a million it becomes a crore. Therefore 1 crore =Ten Million (e) 1 million = Ten lakh. Explanation: 100000 ( 5 Zeroes) 1 lakh 1000000 (6 Zeroes)  one million or ten lakh When we multiply Ten to a Lakh it becomes a million. Therefore 1 million = Ten lakh 2. Place commas correctly and write the numerals:(a) Seventy three lakh seventy five thousand three hundred seven. Answer: 73,75,307 Explanation: The given numeral is according to the Indian system, where the commas are used to denote hundreds, thousands, and lakhs. Thus, Seventy three lakh seventy five thousand three hundred seven is equal to 73,75,307. (b) Nine crore five lakh forty one. Answer: 9,05,00,041 Explanation: The given numeral is according to the Indian system, where the commas are used to denote hundreds, thousands, lakhs, and crores. Thus, Nine crore five lakh forty one is equal to 9,05,00,041. (c) Seven crore fifty two lakh twenty one thousand three hundred two. Answer: 7,52,21,302 Explanation: The given numeral is according to the Indian system, where the commas are used to denote hundreds, thousands, lakhs, and crores. Thus, Seven crore fifty two lakh twenty one thousand three hundred two is equal to 7,52,21,302. (d) Fifty eight million four hundred twenty three thousand two hundred two. Answer: 58,423,202 Explanation: The given numeral is according to the International system, where the commas are inserted after every three digits from the right. It denotes hundreds, thousands, millions, and billions. Thus, Fifty eight million four hundred twenty three thousand two hundred two is equal to 58,423,202. (e) Twenty three lakh thirty thousand ten. Answer: 23, 30, 010 Explanation: The given numeral is according to the Indian system, where the commas are used to denote hundreds, thousands, lakhs, and crores. Thus, Twenty three lakh thirty thousand ten is equal to 23, 30, 010. 3. Insert commas suitably and write the names according to Indian System of Numeration:Explanation: According to the Indian system, the commas are used to denote hundreds, thousands, and lakhs. The first comma comes after the three digits from the right, the second comma comes after the five digits from the right. The third comma comes after the next two digits or seven digits from the right. (a) 87595762 Answer: 8,75,95,762 Name: Eight crores seventy five lakh ninety five thousand seven hundred sixty two. (b) 8546283 Answer: 85,46,283 Name: Eighty five lakh forty six thousand two hundred eightly three (c) 99900046 Answer: 9,99,00,046 Name: Nine crore ninety nine lakh forty six (d) 98432701 Answer: 9,84,32,701 Name: Nine crore eightly four lakh thirty two thousand seven hundred one 4. Insert commas suitably and write the names according to International System of Numeration:Explanation: According to the International system, are used to denote thoudands and millions. The commas are inserted after every three digits from the right. It denotes hundreds, thousand, millions, and billions. (a) 78921092 Answer: 78,921,092 Name: seventy eight million, nine hundred twenty one thousand, ninety two (b) 7452283 Answer: 7,452,283 Name: Seven million four hundred fifty two thousand two hundred eighty three c) 99985102 Answer: 99,985,102 Name: Ninety nine million nine hundred eightly five thousand one hundred two (d) 48049831 Answer: 48,049,831 Name: Forty eight million forty nine thousand eight hundred thirty one Exercise 1.21. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days. Solution: The tickets sold on the first day = 1094 The tickets sold on the second day = 1812 The tickets sold on the third day = 2050 The tickets sold on the final day = 2751 Total number of tickets = 1094 + 1812 + 2050 + 2751 = 7707 Thus, the total number of tickets sold on all the four days is 7707 tickets. 2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need? Solution: Number of runs scored in test matches = 6980 Total number of runs need to be completed = 10000 Runs required = Total runs  scored runs = 10000  6980 = 3020 Thus, shekhar requires 3020 runs to complete 10,000 runs. 3. In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election? Solution: The successful registered votes = 5,77,500 The nearest rival secured votes = 3,48,700 Margin = successful votes  secured votes Margin = 5,77,500  3,48,700 = 2,28,800 Thus, the successful candidate won the election by 2,28,800 votes. 4. Kirti bookstore sold books worth 2,85,891 in the first week of June and booksworth 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much? Solution: Books sold in the first week of the month = 2,85,891 Books sold in the second week of the month = 4,00,768 Total books sold = 2,85,891 + 4,00,768 = 6,86,659 Thus, the toal sale for the two weeks together is 6,86,659. The sale was greater in the second week of the month. Difference = 4,00,768  2,85,891 = 1,14,877 Thus, the sale in the second week is greater by 1,14,877. 5. Find the difference between the greatest and the least 5digit number that can be written using the digits 6, 2, 7, 4, 3 each only once. Solution: The greatest 5digit number that can be written using the digits 6, 2, 7, 4, 3 is 76432. The least 5digit number that can be written using the digits 6, 2, 7, 4, 3 is 23467. Difference = 76432  23467 = 52965 Thus, the difference between the greatest and the least 5digit number that can be written using the digits 6, 2, 7, 4, 3 each only once is 52965. 6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006? Solution: Screws manufactured by a machine a day = 2825 January has 31 number of days Total screws manufactured by a machine in 31 days = 2825 x 31 = 87575 Thus, screws produced by a machine the month of January 2006 is 87,575. 7. A merchant had 78,592 with her. She placed an order for purchasing 40 radio sets at 1200 each. How much money will remain with her after the purchase? Solution: Cost of one radio set = 1200 Cost of 40 radios set = 1200 x 40 = 48,000 Total money with the merchant = 78,592 Money left with merchant = total money  cost of radios = 78,592  48,000 = 30,592 Thus, the money left with the merchant after the purchase is 30,592. 8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications? Solution: Incorrect answer = 7236 × 65 = 470340 Correct answer = 7236 × 56 = 405216 Difference = 470340  405216 Difference = 65124 Thus, his answer was 65124 greater than the correct answer. 9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint: convert data in cm.) Solution: 1m = 100 cm The cloth required to stitch a shirt = 2m 15 cm = 200 + 15 = 215 cm Total available cloth = 40m = 4000 cm Total number of shirts that can be stitched from the 4000 cm cloth are 18. The remained cloth = 130 cm = 1m and 30 cm 10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg? Solution: Weight of a box = 4 kg 500 g 1 kg = 1000 g Total weight of a box = 4000 + 500 = 4500 g Total number of boxes that can be loaded in a van which cannot carry beyond 800 kg = 800 kg/4500 g = 8,00,000g/4500 g Thus, 177 boxes each of weight 4 kg 500g can be loaded in a van which cannot carry beyond 800 kg. The remainder value is less than the weight of a single box. Hence, we will not count it. 11. The distance between the school and a student's house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days. Solution: Distance between the school and a house = 1 km 875 m 1 km = 1000m Total distance covered in 1 way= 1000 + 875 = 1875m Total distance covered in both the ways = 1875 + 1875 = 3750m Total distance covered in 1 day = 3750m Total distance covered in 6 days = 3750 x 6 = 22500m Or 22 km and 500 m Thus, the total distance covered by a student in six days is 22 km and 500 m. 12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled? Solution: Total litres of curd in a vessel = 4 litres and 500 ml 1 litre = 1000 ml 4 litres = 4 x 1000 = 4000 ml Total litres of curd in a vessel = 4500 ml Number of glasses = 4500 ml/25ml = 180 In 180 glasses, each of 25 ml, 4500 ml of curd can be filled. Exercise 1.31. Estimate each of the following using general rule:According to the general rule, We see that the numbers 1,2,3 and 4 are nearer to 0 than to 10. So, we round off 1, 2, 3 and 4 as 0. Number 6, 7, 8, 9 are nearer to 10, so, we round them off as 10. Number 5 is equidistant from both 0 and 10; it is a common practice to round it off as 10. (a) 730 + 998 Answer: 700 + 1000 = 1700 730 is rounded off to 700 998 is rounded off to 1000 (b) 796  314 Answer: 800  300 = 500 796 is rounded off to 800 314 is rounded off to 300 (c) 12,904 + 2,888 Answer: 13000 + 3000 = 16000 12904 is rounded off to 13000 2888 is rounded off to 3000 (d) 28,292  21,496 Answer: 28000  21000 = 7000 28292 is rounded off to 28000 21496 is rounded off to 21000 Make ten more such examples of addition, subtraction and estimation of their outcome. Solution: The ten examples are as follows: 1. 120 + 320 = 100 + 300 = 400 120 is rounded off to 100 320 is rounded off to 300 2. 190 + 170 = 200 + 200 = 400 190 is rounded off to 200 170 is rounded off to 200 3. 2993 + 2878 = 3000 + 3000 = 6000 2993 is rounded off to 3000 2878 is rounded off to 3000 4. 1211 + 4897 = 1000 + 5000 = 6000 1211 is rounded off to 1000 4897 is rounded off to 5000 5. 561 + 222 = 600 + 200 = 800 561 is rounded off to 600 222 is rounded off to 200 6. 987 + 518 = 1000 + 500 = 1500 987 is rounded off to 1000 518 is rounded off to 500 7. 321 + 308 = 300 + 300 = 600 321 is rounded off to 300 308 is rounded off to 300 8. 568 + 456 = 600 + 500 = 1100 568 is rounded off to 600 456 is rounded off to 500 9. 3888 + 2700 = 4000 + 3000 = 7000 3888 is rounded off to 4000 2700 is rounded off to 3000 10. 3113 + 1111 = 3000 + 1000 = 4000 3113 is rounded off to 3000 1111 is rounded off to 1000 2. Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens) :(a) 439 + 334 + 4,317 Answer: Rounding off to nearest hundreds 400 + 300 + 4300 = 5000 439 is rounded off to 400 334 is rounded off to 300 4317 is rounded off to 4300 Rounding off to nearest tens 440 + 330 + 4320 = 5090 439 is rounded off to 440 334 is rounded off to 330 4317 is rounded off to 4320 (b) 1,08,734  47,599 Answer: Rounding off to nearest hundreds 108700  47600 = 61100 108734 is rounded off to 108700 47599 is rounded off to 47600 Rounding off to nearest tens 108730  47600 = 61130 108734 is rounded off to 108730 47599 is rounded off to 47600 (c) 8325  491 Answer: Rounding off to nearest hundreds 8300  500 = 7800 8325 is rounded off to 8300 491 is rounded off to 500 Rounding off to nearest tens 8330  490 = 7840 8325 is rounded off to 8330 491 is rounded off to 490 (d) 4,89,348  48,365 Answer: Rounding off to nearest hundreds 489300  48400 = 440900 489348 is rounded off to 489300 48365 is rounded off to 48400 Rounding off to nearest tens 489350  48370 = 440980 489348 is rounded off to 489350 48365 is rounded off to 48370 Make four more such examples. Solution: The four examples are as follows: 1. 45887  43785 Rounding off to nearest hundreds 45900  43800 = 2100 45887 is rounded off to 45900 43785 is rounded off to 43800 Rounding off to nearest tens 45890  43790 = 2100 45887 is rounded off to 45890 43785 is rounded off to 43790 2. 436 + 574 Rounding off to nearest hundreds 400 + 600 = 1000 436 is rounded off to 400 574 is rounded off to 600 Rounding off to nearest tens 440 + 570 = 1010 436 is rounded off to 440 574 is rounded off to 570 3. 21114 + 4562 Rounding off to nearest hundreds 21100 + 4600 = 25700 21114 is rounded off to 21100 4562 is rounded off to 4600 Rounding off to nearest tens 21110 + 4560 = 25670 21114 is rounded off to 21110 4562 is rounded off to 4560 4. 689  347 Rounding off to nearest hundreds 700 + 300 = 1000 689 is rounded off to 700 347 is rounded off to 300 Rounding off to nearest tens 690 + 350 = 1040 689 is rounded off to 690 347 is rounded off to 350 3. Estimate the following products using general rule:(a) 578 × 161 Answer: 600 × 200 = 120000 578 is rounded off to 600 161 is rounded off to 200 (b) 5281 × 3491 Answer: 5000 × 3500 = 17500000 5281 is rounded off to 5000 3491 is rounded off to 3500 (c) 1291 × 592 Answer: 1300 × 600 = 780000 1291 is rounded off to 1300 592 is rounded off to 600 (d) 9250 × 29 Answer: 9000 × 30 = 270000 9250 is rounded off to 9000 29 is rounded off to 30 Make four more such examples. Solution: The four examples are as follows: 1. 521 × 12 500 × 10 = 5000 2. 456 × 68 500 × 70 = 35000 3. 3312 × 135 3000 × 100 = 300000 4. 789 × 459 800 × 500 = 400000
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