Selina Concise Solutions for ICSE Class 6 Mathematics Chapter 2 Estimation

Estimation

Question. Round off each of the following to the nearest ten:
(i) 62
(ii) 265
(iii) 543
(iv) 8261
(v) 6294
(vi) 3008
(vii) 72326
Answer: 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. Round off each of the following to the nearest hundred :
(i) 748
(ii) 784
(iii) 2667
(iv) 5432
(v) 6388
(vi) 59237
Answer: 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. Round off each of the following to the nearest thousand:
(i) 6475
(ii) 6732
(iii) 5352
(iv) 32568
(v) 9248
(vi) 83294
Answer: 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. 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.
Answer: (i) \( 578 – 580 \)
(ii) \( 578 – 600 \)
(iii) \( 4327 – 4000 \)
(iv) \( 32974 – 30000 \)
(v) \( 27487 – 30000 \)

Question. 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
Answer: (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. Round off the following to the nearest tens ;
(i) Rs. 562
(ii) 837 m
(iii) 545 cm
(iv) Rs. 27
Answer: (i) Rs. 562
\( Rs. 562 – Rs. 560 \)
(ii) 837 m
\( 837 – 840 \text{ m} \)
(iii) 545 cm
\( 545 – 550 \)
(iv) Rs. 21
\( Rs. 27 – Rs. 30 \)

Question. List all the numbers which can be round off to 30.
Answer: The numbers that can be rounded off to 30 are:
26, 27, 28, 29, 31, 32, 33, 34

Question. List all the numbers which can be rounded off to 50.
Answer: The numbers that can be rounded off to 50 are:
46, 47, 48, 49, 51, 52, 53, 54

Question. Write the smallest and the largest numbers which are rounded off to 80.
Answer: The smallest number which is rounded off to 80 is 75
and the largest number which is rounded off to 80 is 84.

Question. Write the smallest and the largest numbers which are rounded off to 130.
Answer: 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. 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
Answer: (i) 67 and 44
67 to the nearest ten 70 and, 44 to the nearest ten = 40
\(\therefore\) Required sum \( (70 + 40) = 110 \)
(ii) 34 and 87
34 to the nearest ten = 30 and, 87 to the nearest ten = 90
\(\therefore\) Required sum \( (30 + 90) = 120 \)
(iii) 23 and 66
23 to the nearest ten = 20 and, 66 to the nearest ten = 70
\(\therefore\) Required sum \( (20 + 70) = 90 \)
(iv) 78 and 18
78 to the nearest ten = 80 and, 18 to the nearest ten = 20
\(\therefore\) Required sum \( (80 + 20) = 100 \)
(v) 96 and 55
96 to the nearest ten = 100 and, 55 to the nearest ten = 60
\(\therefore\) Required sum \( (100 + 60) = 160 \)
(vi) 76 and 62
76 to the nearest ten = 80 and, 62 to the nearest ten = 60
\(\therefore\) Required sum \( (80 + 60) = 140 \)
(vii) 457 and 175
457 to the nearest ten = 460 and, 175 to the nearest ten = 180
\(\therefore\) Required sum \( (460 + 180) = 640 \)
(viii) 474 and 173
474 to the nearest ten = 470 and, 173 to the nearest ten = 170
\(\therefore\) Required sum \( (470 + 170) = 640 \)
(ix) 527 and 267
527 to the nearest ten = 530 and, 267 to the nearest ten = 270
\(\therefore\) Required sum \( (530 + 270) = 800 \)

Question. 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
Answer: (i) 336 and 782
336 to the nearest hundred = 300 and, 782 to the nearest hundred = 800
\(\therefore\) Required sum \( (300 + 800) = 1100 \)
(ii) 546 and 342 and, 342 to the nearest hundred = 300
\(\therefore\) Required sum \( (500 + 300) = 800 \)
(iii) 270 and 495
270 to the nearest hundred = 300 and, 495 to the nearest hundred = 500
\(\therefore\) Required sum \( (300 + 500) = 800 \)
(iv) 4280 and 5295
4280 to the nearest hundred = 4300 and, 5295 to the nearest hundred = 5300
\(\therefore\) Required sum \( (4300 + 5300) = 9600 \)
(v) 4230 and 2410
4230 to the nearest hundred = 4200 and, 2410 to the nearest hundred = 2400
\(\therefore\) Required number \( (4200 + 2400) = 6600 \)
(vi) 30047 and 39287
30047 to the nearest hundred = 30000 and, 39287 to the nearest hundred = 39300
\(\therefore\) Required sum \( (30000 + 39300) = 69, 300 \)

Question. Estimate the sum of the following pair of numbers to the nearest thousand:
(i) 53826 and 36455
(ii) 56802 and 22475
Answer: (i) 53826 and 36455
53826 to the nearest hundred = 54000 and, 36455 to the nearest hundred = 36000
\(\therefore\) Required sum \( (54000 + 36000) = 90000 \)
(ii) 56802 and 22475
56802 to the nearest thousand = 57000 and, 22475 to the nearest thousand = 22000
\(\therefore\) Required sum \( (57000 + 22000) = 79000 \)

Question. Estimate the following differences correct to nearest ten :
(i) 82 – 27
(ii) 96 – 36
(iii) 508 – 248
Answer: (i) 82 – 27
82 to the nearest ten = 80 and, 27 to the nearest ten = 30
\(\therefore\) Required difference \( (80 – 30) = 50 \)
(ii) 96 – 36
96 to the nearest ten = 100 and, 36 to the nearest ten = 40
\(\therefore\) Required difference \( (100 – 40) = 60 \)
(iii) 508 – 248
508 to the nearest ten = 510 and, 248 to the nearest ten = 250
\(\therefore\) Required difference \( (510 – 250) = 260 \)

Question. Estimate each difference to the nearest hundred :
(i) 769 – 314
(ii) 856 – 687
(iii) 6352 – 2086
Answer: (i) 769 – 314
769 to the nearest hundred = 800 and, 314 to the nearest hundred = 300
\(\therefore\) Required difference \( (800 – 300) = 500 \)
(ii) 856 – 687
856 to the nearest hundred = 900 and, 687 to the nearest hundred = 700
\(\therefore\) Required difference \( (900 – 700) = 200 \)
(iii) 6352 – 2086
6352 to the nearest hundred = 6400 and, 2086 to the nearest hundred = 2100
\(\therefore\) Required difference \( (6400 – 2100) = 4300 \)

Question. Estimate each difference to the nearest thousand:
(i) 45974 – 38766
(ii) 76003 – 48399
Answer: (i) 45974 – 38766
45974 to the nearest thousand = 46000 and, 38760 to the nearest thousand = 39000
\(\therefore\) Required difference \( (46000 – 39000) = 7000 \)
(ii) 76003 – 48399
76003 to the nearest thousand = 76000 and, 48399 to the nearest thousand = 48000
\(\therefore\) Required difference \( (76000 – 48000) = 28000 \)

Question. Estimate each of the following products by rounding of each number to the nearest ten :
(i) \( 49 \times 52 \)
(ii) \( 63 \times 38 \)
(iii) \( 27 \times 54 \)
(iv) \( 53 \times 85 \)
(v) \( 74 \times 67 \)
(vi) \( 25 \times 33 \)
Answer: (i) \( 49 \times 52 \)
49 to the nearest ten = 50 and, 52 to the nearest ten = 50
\(\therefore\) Required product \( (50 \times 50) = 2500 \)
(ii) \( 63 \times 38 \)
63 ta the nearest ten = 60 and, 38 to the nearest ten = 40
\(\therefore\) Required product \( (60 \times 40) = 2400 \)
(iii) \( 27 \times 54 \)
27 to the nearest ten = 30 and, 54 to the nearest ten = 50
\(\therefore\) Required product \( (30 \times 50) = 1500 \)
(iv) \( 53 \times 85 \)
53 to the nearest ten = 50 and, 85 to the nearest ten = 90
\(\therefore\) Required product \( (50 \times 90) = 4500 \)
(v) \( 74 \times 67 \)
74 to the nearest ten = 70 and, 67 to the nearest ten = 70
\(\therefore\) Required product \( (70 \times 70) = 4900 \)
(vi) \( 25 \times 33 \)
25 to the nearest ten = 30 and, 33 to the nearest ten = 30
\(\therefore\) Required product \( (30 \times 30) = 900 \)

Question. Estimate each of the following products by rounding off each number to the nearest hundred :
(i) \( 477 \times 213 \)
(ii) \( 624 \times 236 \)
(iii) \( 333 \times 247 \)
(iv) \( 537 \times 283 \)
(v) \( 382 \times 127 \)
(vi) \( 427 \times 328 \)
Answer: (i) \( 477 \times 213 \)
477 to the nearest hundred = 500 and, 213 to the nearest hundred = 200
\(\therefore\) Required product \( (500 \times 200) = 100000 \)
(ii) \( 624 \times 236 \)
624 to the nearest hundred = 600 and, 236 to the nearest hundred = 200
\(\therefore\) Required product \( (600 \times 200) = 120000 \)
(iii) \( 333 \times 247 \)
333 to the nearest hundred = 300 and, 247 to the nearest hundred = 200
\(\therefore\) Required product \( (300 \times 200) = 60000 \)
(iv) \( 537 \times 283 \)
537 to the nearest hundred = 500 and, 283 to the nearest hundred = 300
\(\therefore\) Required product \( (500 \times 300) = 150000 \)
(v) \( 382 \times 127 \)
382 to the nearest hundred = 400 and, 127 to the nearest hundred = 100
\(\therefore\) Required product \( (400 \times 100) = 40000 \)
(vi) \( 427 \times 328 \)
472 to the nearest hundred = 500 and, 328 to the nearest hundred = 300
\(\therefore\) Required product \( (500 \times 300) = 150000 \)

Question. 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) \( 28 \times 287 \)
(ii) \( 432 \times 128 \)
(iii) \( 48 \times 165 \)
(iv) \( 72 \times 258 \)
(v) \( 83 \times 664 \)
(vi) \( 44 \times 250 \)
Answer: (i) \( 28 \times 287 \)
28 to the nearest ten = 30 and, 287 to the nearest hundred = 300
\(\therefore\) Required product \( (30 \times 300) = 9000 \)
(ii) \( 432 \times 128 \)
432 to the nearest ten = 430 and, 128 to the nearest hundred = 100
\(\therefore\) Required product \( (430 \times 100) = 43000 \)
(iii) \( 48 \times 165 \)
48 to the nearest ten = 50 and, 165 to the nearest hundred = 200
\(\therefore\) Required product \( (50 \times 200) = 10000 \)
(iv) \( 72 \times 258 \)
72 to the nearest ten = 70 and, 258 to the nearest hundred = 300
\(\therefore\) Required product \( (70 \times 300) = 21000 \)
(v) \( 83 \times 664 \)
83 to the nearest ten = 80 and, 664 to the nearest hundred = 700
\(\therefore\) Required product \( (80 \times 700) = 56000 \)
(vi) \( 44 \times 250 \)
44 to the nearest ten = 40 and, 250 to the nearest hundred = 300
\(\therefore\) Required product \( (40 \times 300) = 12000 \)

Question. Estimate each of the following quotients by converting each number to the nearest ten :
(i) \( 87 \div 28 \)
(ii) \( 84 \div 23 \)
(iii) \( 77 \div 22 \)
(iv) \( 198 \div 24 \)
(v) \( 355 \div 26 \)
(vi) \( 444 \div 42 \)
(vii) \( 843 \div 33 \)
Answer: (i) \( 87 \div 28 \)
\( (87 \div 28) \) is (approximately to the nearest 10) equal to \( 90 \div 30 = 3 \)
(ii) \( 84 \div 23 \)
\( 84 \div 23 \) is (approximately to the nearest 10) equal to \( 80 \div 20 = 4 \)
(iii) \( 77 \div 22 \)
\( 77 \div 22 \) is (approximately to the nearest 10) equal to \( 80 \div 20 = 4 \)
(iv) \( 198 \div 24 \)
\( 198 \div 24 \) is (approximately to the nearest 10) equal to \( 200 \div 20 = 10 \)
(v) \( 355 \div 26 \)
\( 355 \div 26 \) is (approximately to the nearest 10) equal to \( 360 \div 30 = 12 \)
(vi) \( 444 \div 42 \)
\( 444 \div 42 \) is (approximately to the nearest 10) equal to \( 440 \div 40 = 11 \)
(vii) \( 843 \div 33 \)
\( 843 \div 33 \) is (approximately to the nearest 10) equal to \( 840 \div 30 = 28 \)