## NCERT Solutions Class 6 Maths## Chapter - 1: Knowing our Numbers## Exercise 1.1## 1. Fill in the blanks:
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
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
1000000 (6 Zeroes) - one million or ten lakh Multiply by ten we get: 10000000 (7 Zeroes) - 1 crore
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
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.
Thus, Seventy three lakh seventy five thousand three hundred seven is equal to 73,75,307. (b) Nine crore five lakh forty one.
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.
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.
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.
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:
(a) 87595762
(b) 8546283
(c) 99900046
(d) 98432701
## 4. Insert commas suitably and write the names according to International System of Numeration:
(a) 78921092
(b) 7452283
c) 99985102
(d) 48049831
## 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.
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 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?
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 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?
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 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?
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 The sale was greater in the Difference = 4,00,768 - 2,85,891 = 1,14,877 Thus, the sale in the second week is greater by 5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.
The greatest 5-digit number that can be written using the digits 6, 2, 7, 4, 3 is 76432. The least 5-digit 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 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once is 6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
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?
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 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?
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.)
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
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?
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.
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
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?
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 ## Exercise 1.3## 1. 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
730 is rounded off to 700 998 is rounded off to 1000 (b) 796 - 314
796 is rounded off to 800 314 is rounded off to 300 (c) 12,904 + 2,888
12904 is rounded off to 13000 2888 is rounded off to 3000 (d) 28,292 - 21,496
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.
The ten examples are as follows:
120 is rounded off to 100 320 is rounded off to 300
190 is rounded off to 200 170 is rounded off to 200
2993 is rounded off to 3000 2878 is rounded off to 3000
1211 is rounded off to 1000 4897 is rounded off to 5000
561 is rounded off to 600 222 is rounded off to 200
987 is rounded off to 1000 518 is rounded off to 500
321 is rounded off to 300 308 is rounded off to 300
568 is rounded off to 600 456 is rounded off to 500
3888 is rounded off to 4000 2700 is rounded off to 3000
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
400 + 300 + 4300 = 5000 439 is rounded off to 400 334 is rounded off to 300 4317 is rounded off to 4300
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
108700 - 47600 = 61100 108734 is rounded off to 108700 47599 is rounded off to 47600
108730 - 47600 = 61130 108734 is rounded off to 108730 47599 is rounded off to 47600 (c) 8325 - 491
8300 - 500 = 7800 8325 is rounded off to 8300 491 is rounded off to 500
8330 - 490 = 7840 8325 is rounded off to 8330 491 is rounded off to 490 (d) 4,89,348 - 48,365
489300 - 48400 = 440900 489348 is rounded off to 489300 48365 is rounded off to 48400
489350 - 48370 = 440980 489348 is rounded off to 489350 48365 is rounded off to 48370 Make four more such examples.
The four examples are as follows:
45900 - 43800 = 2100 45887 is rounded off to 45900 43785 is rounded off to 43800
45890 - 43790 = 2100 45887 is rounded off to 45890 43785 is rounded off to 43790
400 + 600 = 1000 436 is rounded off to 400 574 is rounded off to 600
440 + 570 = 1010 436 is rounded off to 440 574 is rounded off to 570
21100 + 4600 = 25700 21114 is rounded off to 21100 4562 is rounded off to 4600
21110 + 4560 = 25670 21114 is rounded off to 21110 4562 is rounded off to 4560
700 + 300 = 1000 689 is rounded off to 700 347 is rounded off to 300
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
578 is rounded off to 600 161 is rounded off to 200 (b) 5281 × 3491
5281 is rounded off to 5000 3491 is rounded off to 3500 (c) 1291 × 592
1291 is rounded off to 1300 592 is rounded off to 600 (d) 9250 × 29
9250 is rounded off to 9000 29 is rounded off to 30
The four examples are as follows:
500 × 10 = 5000
500 × 70 = 35000
3000 × 100 = 300000
800 × 500 = 400000 Next TopicNCERT Solutions Class 6 Maths Chapter 2 |