Knowing Our Numbers (Mathematics) Class 6 - NCERT Questions

Fill in the blanks:

(A) 1 lakh = _______ ten thousand.

(B) 1 million = _______ hundred thousand.

(C) 1 crore = _______ ten lakh.

(D) 1 crore = _______ million.

(E) 1 million = _______ lakh.

(A) 10 : 1 lakh = 1,00,000

= 10 × 10,000 = 10 ten thousand

(B) 10 : 1 million = 1,000,000

= 10 × 100,000 = 10 hundred thousand

(C) 10 : 1 crore = 1,00,00,000

= 10 × 10,00,000 = 10 ten lakh

(D) 10 : 1 crore = 10 million

(E) 10 : 1 million = 10 lakh

Place commas correctly and write the numerals:

(A) Seventy three lakh seventy five thousand three hundred seven.

(B) Nine crore five lakh forty one.

(C) Seven crore fifty two lakh twenty one thousand three hundred two.

(D) Fifty eight million four hundred twenty three thousand two hundred two.

(E) Twenty three lakh thirty thousand ten.

(A) 73,75,307

(B) 9,05,00,041

(C) 7,52,21,302

(D) 58,423,202

(E) 23,30,010

Insert commas suitably and write the names according to Indian System of Numeration :

(A) 87595762

(B) 8546283

(C) 99900046

(D) 98432701

(A) 8,75,95,762 → Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two.

(B) 85,46,283 → Eighty-five lakh forty-six thousand two hundred eighty-three.

(C) 9,99,00,046 → Nine crore ninety-nine lakh forty-six.

(D) 9,84,32,701 → Nine crore eighty-four lakh thirty-two thousand seven hundred one.

Insert commas suitably and write the names according to International System of Numeration:

(A) 78921092

(B) 7452283

(C) 99985102

(D) 48049831

(A) 78,921,092 → Seventy-eight million nine hundred twenty-one thousand ninety-two

(B) 7,452,283 → Seven million four hundred fifty-two thousand two hundred eighty-three

(C) 99,985,102 → Ninety-nine million nine hundred eighty-five thousand one hundred two

(D) 48,049,831 → Forty-eight million forty-nine thousand eight hundred thirty-one

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:Number of tickets sold on first day = 1,094

Number of tickets sold on second day = 1,812

Number of tickets sold on third day = 2,050

Number of tickets sold on fourth day = 2,751

Total tickets sold = 1,094 + 1,812 + 2,050 + 2,751

= 7,707

Therefore, 7,707 tickets were sold on all the four days.

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 to achieve = 10,000

Number of runs scored = 6,980

Number of runs required = 10,000 - 6,980 = 3,020

Therefore, Shekhar needs 3,020 more runs.

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:Number of votes secured by successful candidate = 5,77,500

Number of votes secured by his nearest rival = 3,48,700

Margin between them = 5,77,500 - 3,48,700

= 2,28,800

Therefore, the successful candidate won by a margin of 2,28,800 votes.

Kirti bookstore sold books worth Rs 2,85,891 in the first week of June and books worth

Rs 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?

Worth of books sold in first week = Rs 2,85,891

Worth of books sold in second week = Rs 4,00,768

Total worth of books sold = Rs (2,85,891 + 4,00,768)

= Rs 6,86,659

Since, 4,00,768 > 2,85,891

Therefore, sale of second week is greater than that of first week by Rs (4,00,768 - 2,85,891)

= Rs 1,14,877

Find the difference between the greatest and the least number that can be written using the digits 6, 2, 7, 4, 3 each only once.

SOLUTION:Greatest five-digit number using digits

6,2,7,4,3 = 76432

Smallest five-digit number using digits

6,2,7,4,3 = 23467

Difference = 76432 - 23467 = 52965

Therefore, the difference is 52,965.

A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

SOLUTION:Number of screws manufactured in one day = 2,825

Number of screws manufactured in the month of January (31 days) = 2,825 × 31 = 87,575

Therefore, the machine produced 87,575 screws in the month of January.

A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?

SOLUTION:Cost of one radio set = Rs 1200

Cost of 40 radio sets = Rs (1200 × 40) = Rs 48,000

Now, total money with merchant = Rs 78,592

Money left with her = Rs (78,592 - 48,000)

= Rs 30,592

Therefore, Rs 30,592 will remain with her after the purchase.

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:Q 13.

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.)

Cloth required to stitch one shirt

= 2 m 15 cm = 2 × 100 cm + 15 cm = 215 cm

Length of cloth = 40 m = 40 × 100 cm = 4000 cm

Number of shirts can be stitched = 4000 ÷ 215

Therefore, 18 shirts can be stitched and 130 cm (1 m 30 cm) cloth will remain.

Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?

SOLUTION:The weight of one box = 4 kg 500 g

= 4 × 1000 g + 500 g = 4500 g

Maximum load can be loaded in a van

= 800 kg = 800 × 1000 g = 800000 g

Number of boxes = 800000 ÷ 4500

Therefore, 177 boxes can be loaded in the van.

The distance between the school and the house of a student 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 house

= 1 km 875 m = 1 km + 875/1000 km = 1.875 km

Total distance covered in one day

= (1.875 × 2)km = 3.750 km

Distance covered in six days = (3.750 × 6) km

= 22.500 km

Therefore, a student covered 22 km 500 m distance in six days.

A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?

SOLUTION:Quantity of curd in the vessel

= 4 litres 500 ml = 4 × 1000 ml + 500 ml

= 4500 ml

Capacity of one glass = 25 ml

Number of glasses can be filled = 4500 ÷ 25

Therefore, 180 glasses can be filled by curd.

Estimate each of the following using general rule:

(A) 730 + 998

(B) 796 - 314

(C) 12,904 + 2,888

(D) 28,292 - 21,496

Make ten more such examples of addition, subtraction and estimation of their outcome.

(A) 730 rounds off to 700

998 rounds off to 1,000

∴ Estimated sum = 700 + 1,000 = 1,700

(B) 796 rounds off to 800

314 rounds off to 300

∴ Estimated difference = 800 - 300 = 500

(C) 12,904 rounds off to 13,000

2,888 rounds off to 3,000

∴ Estimated sum = 13,000 + 3,000 = 16,000

(D) 28,292 rounds off to 28,000

21,496 rounds off to 21,000

∴ Estimated difference = 28,000 - 21,000

= 7,000

Ten more examples:

(I) 540 + 868

540 rounds off to 500

868 rounds off to 900

∴ Estimated sum = 500 + 900 = 1,400

(ii) 1,369 + 215

1,369 rounds off to 1,000

215 rounds off to 200

∴ Estimated sum = 1,000 + 200 = 1,200

(iii) 46,352 - 11,867

46,352 rounds off to 46,000

11,867 rounds off to 12,000

∴ Estimated difference = 46,000 - 12,000

= 34,000

(iv) 14,902 + 6,565

14,902 rounds off to 15,000

6,565 rounds off to 7,000

∴ Estimated sum = 15,000 + 7,000 = 22,000

(v) 514 - 386

514 rounds off to 500

386 rounds off to 400

∴ Estimated difference = 500 - 400 = 100

(vi) 27,904 + 69,592

27,904 rounds off to 28,000

69,592 rounds off to 70,000

∴ Estimated sum = 28,000 + 70,000 = 98,000

(vii) 530 - 98

530 rounds off to 500

98 rounds off to 100

∴ Estimated difference = 500 - 100 = 400

(viii) 18,230 - 3,666

18,230 rounds off to 18,000

3,666 rounds off to 4,000

∴ Estimated difference = 18,000 - 4,000

= 14,000

(ix) 56,306 + 17,693

56,306 rounds off to 56,000

17,693 rounds off to 18,000

∴ Estimated sum = 56,000 + 18,000 = 74,000

(x) 4,275 - 125

4,275 rounds off to 4,000

125 rounds off to 100

∴ Estimated difference = 4,000 - 100 = 3,900

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

(B) 1,08,734 - 47,599

(C) 8,325 - 491

(D) 4,89,348 - 48,365

Make four more such examples.

By rounding off to nearest hundreds, we get

439 rounds off to 400

334 rounds off to 300

4,317 rounds off to 4,300

∴ Estimated sum = 400 + 300 + 4,300 = 5,000

By rounding off to nearest tens, we get

439 rounds off to 440

334 rounds off to 330

4,317 rounds off to 4,320

∴ Estimated sum = 440 + 330 + 4,320 = 5,090

(B) By rounding off to nearest hundreds,

we get

1,08,734 rounds off to 1,08,700

47,599 rounds off to 47,600

∴ Estimated difference = 1,08,700 - 47,600

= 61,100

By rounding off to nearest tens, we get

1,08,734 rounds off to 1,08,730

47,599 rounds off to 47,600

∴ Estimated difference = 1,08,730 - 47,600

= 61,130

(C) By rounding off to nearest hundreds, we get

8,325 rounds off to 8,300

491 rounds off to 500

∴ Estimated difference = 8,300 - 500 = 7,800

By rounding off to nearest tens, we get

8,325 rounds off to 8,330

491 rounds off to 490

∴ Estimated difference = 8,330 - 490 = 7,840

(D) By rounding off to nearest hundreds,

we get

4,89,348 rounds off to 4,89,300

48,365 rounds off to 48,400

∴ Estimated difference = 4,89,300 - 48,400

= 4,40,900

By rounding off to nearest tens, we get

4,89,348 rounds off to 4,89,350

48,365 rounds off to 48,370

∴ Estimated difference = 4,89,350 - 48,370

= 4,40,980

Four more examples:

(I) 5,235 - 382

By rounding off to nearest hundreds, we get

5,235 rounds off to 5,200

382 rounds off to 400

∴ Estimated difference = 5,200 - 400 = 4,800

Now, by rounding off to nearest tens, we get

5,235 rounds off to 5,240

382 rounds off to 380

∴ Estimated difference = 5,240 - 380 = 4,860

(ii) 7,673 + 436 + 169

By rounding off to nearest hundreds, we get

7,673 rounds off to 7,700

436 rounds off to 400

169 rounds off to 200

∴ Estimated sum = 7,700 + 400 + 200 = 8,300

Now, by rounding off to nearest tens, we get

7,673 rounds off to 7,670

436 rounds off to 440

169 rounds off to 170

∴ Estimated sum = 7,670 + 440 + 170 = 8,280

(iii) 2,05,290 - 17,986

By rounding off to nearest hundreds, we get

2,05,290 rounds off to 2,05,300

17,986 rounds off to 18,000

∴ Estimated difference = 2,05,300 - 18,000

= 1,87,300

By rounding off to nearest tens, we get

2,05,290 rounds off to 2,05,290

17,986 rounds off to 17,990

∴ Estimated difference = 2,05,290 - 17,990

= 1,87,300

(iv) 6,830 + 35,764

By rounding off to nearest hundreds,

we get

6,830 rounds off to 6,800

35,764 rounds off to 35,800

∴ Estimated sum = 6,800 + 35,800 = 42,600

Now, by rounding off to nearest tens, we get

6,830 rounds off to 6,830

35,764 rounds off to 35,760

∴ Estimated sum = 6,830 + 35,760 = 42,590

Estimate the following products using general rule:

(A) 578 × 161

(B) 5281 × 3491

(C) 1291 × 592

(D) 9250 × 29

Make four more such examples.

(A) 578 × 161

578 rounds off to 600

161 rounds off to 200

∴ The estimated product = 600 × 200 = 1,20,000

(B) 5281 × 3491

5281 rounds off to 5,000

3491 rounds off to 3,000

∴ The estimated product

= 5,000 × 3,000 = 1,50,00,000

(C) 1291 × 592

1291 rounds off to 1,000

592 rounds off to 600

∴ The estimated product

= 1,000 × 600 = 6,00,000

(D) 9250 × 29

9250 rounds off to 9,000

29 rounds off to 30

∴ The estimated product = 9,000 × 30 = 2,70,000

Four more examples:

(I) 3260 × 86

3260 rounds off to 3,000

86 rounds off to 90

∴ Estimated product = 3,000 × 90 = 2,70,000

(ii) 7451 × 4,632

7451 rounds off to 7,000

4632 rounds off to 5,000

∴ Estimated product = 7,000 × 5,000 = 3,50,00,000

(iii) 356 × 204

356 rounds off to 400

204 rounds off to 200

∴ Estimated product = 400 × 200 = 80,000

(iv) 9860 × 692

9860 rounds off to 10,000

692 rounds off to 700

∴ Estimated product = 10,000 × 700 = 70,00,000