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