NCERT Solutions Class 6 Maths
Chapter - 1: Knowing our Numbers
Exercise 1.1
1. 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 1.2
1. 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 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.
Solution:
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 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 1.3
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
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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