**Selina Concise Mathematics Class 6 ICSE Solutions – Estimation**

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**EXERCISE 2(A)**

**Question 1.**

Round off each of the following to the nearest ten :

(i) 62

(ii) 265

(iii) 543

(iv) 8261

(v) 6294

(vi) 3008

(vii) 72326

**Solution:**

If the digit at ones place is less than 5, replace ones digit by 0, and keep the other digit as they are :

And if the digit at ones place is 5 or more than 5, increase tens digit by 1, and replace ones digit by 0.

(i) 62 – 60

(ii) 265 – 270

(iii) 543 – 540

(iv) 8261 – 8260

(v) 6294 – 6290

(vi) 3008-3010

**Question 2.**

Round off each of the following to the nearest hundred :

(i) 748

(ii) 784

(iii) 2667

(iv) 5432

(v) 6388

(vi) 59237

**Solution:**

If the tens digit is less than 5, replace each one of tens and once digits by 0 and keep the other digits as they are :

(i) 748 – 700

(ii) 784 – 800

(iii) 2667 – 2700

(iv) 5432 – 5400

(v) 6388 – 6400

(vi) 59237 – 59200

**Question 3.**

Round off each of the following to the nearest thousand :

(i) 6475

(ii) 6732

(iii) 5352

(iv) 32568

(v) 9248

(vi) 83294

**Solution:**

If the tens digit is 5 or more than 5, increase the hundreds digit by 1 and replace each of tens digit and ones digit by 0.

(i) 6475 – 6000

(ii) 6732 – 7000

(iii) 25352 – 25000

(iv) 32568 – 33000

(v) 9248 – 9000

(vi) 83294 – 83000

**Question 4.**

Round off

(i) 578 to the nearest ten.

(ii) 578 to the nearest hundred.

(iii) 4327 to the nearest thousand.

(iv) 32974 to the nearest ten-thousand.

(v) 27487 to the nearest ten-thousand.

**Solution:**

(i) 578 – 580

(ii) 578 – 600

(iii) 4327 – 4000

(iv) 32974 – 30000

(v) 27487 – 30000

**Question 5.**

Round off each of the following to the nearest tens, hundreds and thousands.

(i) 864

(ii) 1249

(iii) 54, 547

(iv) 68, 076

(v) 56, 293

(vi) 7, 293

(vii) 89, 24, 379

**Solution:**

(i) 864 – 860

864 – 900

864 – 1000

(ii) 1249 – 1250

1249 – 1200

1249 – 1000

(iii) 54, 547 – 54550

54, 547 – 54500

54, 547 – 55000

(iv) 68, 076 – 68, 080

68, 076 – 68, 100

68, 076 – 68, 000

(v) 56, 293 – 56, 290

56, 293 – 56, 300

56, 293 – 56, 000

(vi) 7, 293 – 7290

7, 293 – 7, 300

7, 293 – 7000

(vii) 89, 24, 379 – 89, 24, 380

89, 24, 379 – 89, 24, 400

89, 24, 379 – 89, 24, 000

**Question 6.**

Round off the following to the nearest tens ;

(i) ₹ 562

(ii) 837 m

(iii) 545 cm

(iv) ₹ 27

**Solution:**

(i) ₹ 562

₹ 562 – ₹ 560

(ii) 837 m

837 – 840 m

(iii) 545 cm

545 – 550

(iv) ₹ 21

₹ 27 – ₹ 30

**Question 7.**

List all the numbers which can be round off to 30.

**Solution:**

The numbers that can be rounded off to 30 are:

26, 27, 28, 29, 31, 32, 33, 34

**Question 8.**

List all the numbers which can be rounded off to 50.

**Solution:**

The numbers that can be rounded off to 50 are:

46, 47, 48, 49, 51, 52, 53, 54

**Question 9.**

Write the smallest and the largest numbers which are rounded off to 80.

**Solution:**

The smallest number which is rounded off to 80 is 75

and the largest number which is rounded off to 80 is 84.

**Question 10.**

Write the smallest and the largest numbers which are rounded off to 130.

**Solution:**

The smallest number which is rounded off to 130 is 125

and The largest number which is rounded off to 130 is 134.

**EXERCISE 2(B)**

**Question 1.**

Estimate the sum of each pair of numbers to the nearest ten :

(i) 67 and 44

(ii) 34 and 87

(iii) 23 and 66

(iv) 78 and 18

(v) 96 and 55

(vi) 76 and 62

(vii) 457 and 175

(viii) 474 and 173

(ix) 527 and 267

**Solution:**

(i) 67 and 44

67 to the nearest ten 70 and, 44 to the nearest ten = 40

∴ Required sum (70 + 40) = 110

(ii) 34 and 87

34 to the nearest ten = 30 and, 87 to the nearest ten = 90

∴ Required sum = (30 + 90) = 120

(iii) 23 and 66

23 to the nearest ten = 20 and, 66 to the nearest ten = 70

∴ Required sum = (20 + 70) = 90

(iv) 78 and 18

78 to the nearest ten = 80 and, 18 to the nearest ten = 20

∴ Required sum = (80 + 20) = 100

(v) 96 and 55

96 to the nearest ten = 100 and, 55 to the nearest ten = 60

∴ Required sum = (100 + 60) = 160

(vi) 76 and 62

76 to the nearest ten = 80 and, 62 to the nearest ten = 60

∴ Required sum = (80 + 60) = 140

(vii) 457 and 175

457 to the nearest ten = 460 and, 175 to the nearest ten = 180

∴ Required sum = (460 + 180) = 640

(viii) 474 and 173

474 to the nearest ten = 470 and, 173 to the nearest ten = 170

∴ Required sum = (470 + 170) = 640

(ix) 527 and 267

527 to the nearest ten = 530 and, 267 to the nearest ten = 270

∴ Required sum = (530 + 270) = 800

**Question 2.**

Estimate the sum of each pair of numbers to the nearest hundred :

(i) 336 and 782

(ii) 546 and 342

(iii) 270 and 495

(iv) 4280 and 5295

(v) 4230 and 2410

(vi) 30047 and 39287

**Solution:**

(i) 336 and 782

336 to the nearest hundred = 300 and, 782 to the nearest hundred = 800

∴ Required sum = (300 + 800) = 1100

(ii) 546 and 342 and, 342 to the nearest hundred = 300

∴ Required sum = (500 + 300) = 800

(iii) 270 and 495

270 to the nearest hundred = 300 and, 495 to the nearest hundred = 500

∴ Required sum = (300 + 500) = 800

(iv) 4280 and 5295

4280 to the nearest hundred = 4300 and, 5295 to the nearest hundred = 5300

∴ Required sum = (4300 + 5300) = 9600

(v) 4230 and 2410

4230 to the nearest hundred = 4200 and, 2410 to the nearest hundred = 2400

∴ Required number = (4200 + 2400) = 6600

(vi) 30047 and 39287

30047 to the nearest hundred = 30000 and, 39287 to the nearest hundred = 39300

∴ Required sum = (30000 + 39300) = 69, 300

**Question 3.**

Estimate the sum of the following pair of numbers to the nearest thousand:

(i) 53826 and 36455

(ii) 56802 and 22475

**Solution:**

(i) 53826 and 36455

53826 to the nearest hundred = 54000 and, 36455 to the nearest hundred = 36000

∴ Required sum = (54000 + 36000) = 90000

(ii) 56802 and 22475

56802 to the nearest thousand = 57000 and, 22475 to the nearest thousand = 22000

∴ Required sum = (57000 + 22000) = 79000

**Question 4.**

Estimate the following differences correct to nearest ten :

(i) 82 – 27

(ii) 96 – 36

(iii) 508 – 248

**Solution:**

(i) 82 – 27

82 to the nearest ten = 80 and, 27 to the nearest ten = 30

∴ Required difference = (80 – 30) = 50

(ii) 96 – 36

96 to the nearest ten = 100 and, 36 to the nearest ten = 40

∴ Required difference = (100 – 40) = 60

(iii) 508 – 248

508 to the nearest ten = 510 and, 248 to the nearest ten = 250

∴ Required difference = (510 – 250) = 260

**Question 5.**

Estimate each difference to the nearest hundred :

(i) 769 – 314

(ii) 856 – 687

(iii) 6352 – 2086

**Solution:**

(i) 769 – 314

769 to the nearest hundred = 800 and, 314 to the nearest hundred = 300

∴ Required difference = (800 – 300) = 500

(ii) 856 – 687

856 to the nearest hundred = 900 and, 687 to the nearest hundred = 700

∴ Required difference = (900 – 700) = 200

(iii) 6352 – 2086

6352 to the nearest hundred = 6400 and, 2086 to the nearest hundred = 2100

∴ Required difference = (6400 – 2100) = 4300

**Question 6.**

Estimate each difference to the nearest thousand :

(i) 45974 – 38766

(ii) 76003 – 48399

**Solution:**

(i) 45974 – 38766

45974 to the nearest thousand = 46000 and, 38760 to the nearest thousand = 39000

∴ Required difference = (46000 – 39000) = 7000

(ii) 76003 – 48399

76003 to the nearest thousand = 76000 and, 48399 to the nearest thousand = 48000

∴ Required difference = (76000 – 48000) = 28000

**Question 7.**

Estimate each of the following products by rounding of each number to the nearest ten :

(i) 49 x 52

(ii) 63 x 38

(iii) 27 x 54

(iv) 53 x 85

(v) 74 x 67

(vi) 25 x 33

**Solution:**

(i) 49 x 52

49 to the nearest ten = 50 and, 52 to the nearest ten = 50

∴ Required product = (50 x 50) = 2500

(ii) 63 x 38

63 ta the nearest ten = 60 and, 38 to the nearest ten = 40

∴ Required product = (60 x 40) = 2400

(iii) 27 x 54

27 to the nearest ten = 30 and, 54 to the nearest ten = 50

∴ Required product = (30 x 50) = 1500

(iv) 53 x 85

53 to the nearest ten = 50 and, 85 to the nearest ten = 90

∴ Required product = (50 x 90) = 4500

(v) 74 x 67

74 to the nearest ten = 70 and, 67 to the nearest ten = 70

∴ Required product = (70 x 70) = 4900

(vi) 25 x 33

25 to the nearest ten = 30 and, 33 to the nearest ten = 30

∴ Required product = (30 x 30) = 900

**Question 8.**

Estimate each of the following products by rounding off each number to the nearest hundred :

(i) 477 x 213

(ii) 624 x 236

(iii) 333 x 247

(iv) 537 x 283

(v) 382 x 127

(vi) 427 x 328

**Solution:**

(i) 477 x 213

477 to the nearest hundred = 500 and, 213 to the nearest hundred = 200

∴ Required product = (500 x 200) = 100000

(ii) 624 x 236

624 to the nearest hundred = 600 and, 236 to the nearest hundred = 200

∴ Required product = (600 x 200) = 120000

(iii) 333 x 247

333 to the nearest hundred = 300 and, 247 to the nearest hundred = 200

∴ Required product = (300 x 200) = 60000

(iv) 537 x 283

537 to the nearest hundred = 500 and, 283 to the nearest hundred = 300

∴ Required product = (500 x 300) = 150000

(v) 382 x 127

382 to the nearest hundred = 400 and, 127 to the nearest hundred = 100

∴ Required product = (400 x 100) = 40000

(vi) 427 x 328

472 to the nearest hundred = 500 and, 328 to the nearest hundred = 300

∴ Required product = (500 x 300) = 150000

**Question 9.**

Estimate each of the following products by rounding off the first number correct to nearest ten and the other number correct to nearest hundred :

(i) 28 x 287

(ii) 432 x 128

(iii) 48 x 165

(iv) 72 x 258

(v) 83 x 664

(vi) 44 x 250

**Solution:**

(i) 28 x 287

28 to the nearest ten = 30 and, 287 to the nearest hundred = 300

∴ Required product = (30 x 300) = 9000

(ii) 432 x 128

432 to the nearest ten = 430 and, 128 to the nearest hundred = 100

∴ Required product = (430 x 100) = 43000

(iii) 48 x 165

48 to the nearest ten = 50 and, 165 to the nearest hundred = 200

∴ Required product = (50 x 200) = 10000

(iv) 72 x 258

72 to the nearest ten = 70 and, 258 to the nearest hundred = 300

∴ Required product = (70 x 300) = 21000

(v) 83 x 664

83 to the nearest ten = 80 and, 664 to the nearest hundred = 700

∴ Required product = (80 x 700) = 56000

(vi) 44 x 250

44 to the nearest ten = 40 and, 250 to the nearest hundred = 300

∴ Required product = (40 x 300) = 12000

**Question 10.**

Estimate each of the following quotients by converting each number to the nearest ten :

(i) 87 ÷ 28

(ii) 84 ÷ 23

(iii) 77 ÷ 22

(iv) 198 ÷ 24

(v) 355 ÷ 26

(vi) 444 ÷ 42

(vii) 843 ÷ 33

**Solution:**

(i) 87 ÷ 28

(87 ÷ 28) is (approximately to the nearest 10) equal to 90 ÷ 30 = 3

(ii) 84 ÷ 23

84 ÷ 23 is (approximately to the nearest 10) equal to 80 ÷ 20 = 4

(iii) 77 ÷ 22

77 ÷ 22 is (approximately to the nearest 10) equal to 80 ÷ 20 = 4

(iv) 198 ÷ 24

198 ÷ 24 is (approximately to the nearest 10) equal to 200 ÷ 20 = 10

(v) 355 ÷ 26

355 ÷ 26 is (approximately to the nearest 10) equal to 360 ÷ 30 = 12

(vi) 444 ÷ 42

444 ÷ 42 is (approximately to the nearest 10) equal to 440 ÷ 40 = 11

(vii) 843 ÷ 33

843 ÷ 33 is (approximately to the nearest 10) equal to 840 ÷ 30 = 28

Selina Class 6 Maths ICSE SolutionsPhysicsChemistryBiologyGeographyHistory & Civics

Honey says

It helped me a lot to solve my problems ☺☺

inder says

I am bit confused ,why we are not first adding the numbers then estimating the sum (rounding off the addition).