Estimate the sum after rounding off each pair of numbers to the nearest ten:
(i) 34 and 87
(ii) 78 and 18
(iii) 96 and 55
(iv) 76 and 62
(v) 457 and 175
(vi) 527 and 267
Answer
(i) 34 → 30 and 87 → 90.
Required sum = 30 + 90 = 120.
(ii) 78 → 80 and 18 → 20.
Required sum = 80 + 20 = 100.
(iii) 96 → 100 and 55 → 60.
Required sum = 100 + 60 = 160.
(iv) 76 → 80 and 62 → 60.
Required sum = 80 + 60 = 140.
(v) 457 → 460 and 175 → 180.
Required sum = 460 + 180 = 640.
(vi) 527 → 530 and 267 → 270.
Required sum = 530 + 270 = 800.
Estimate the sum after rounding off each pair of numbers to the nearest hundred:
(i) 336 and 782
(ii) 270 and 495
(iii) 4280 and 5295
(iv) 30047 and 39287
Answer
(i) 336 → 300 and 782 → 800.
Required sum = 300 + 800 = 1100.
(ii) 270 → 300 and 495 → 500.
Required sum = 300 + 500 = 800.
(iii) 4280 → 4300 and 5295 → 5300.
Required sum = 4300 + 5300 = 9600.
(iv) 30047 → 30000 and 39287 → 39300.
Required sum = 30000 + 39300 = 69300.
Estimate the sum after rounding off the following pairs of numbers to the nearest thousand:
(i) 53826 and 36455
(ii) 56802 and 22475
Answer
(i) 53826 → 54000 and 36455 → 36000.
Required sum = 54000 + 36000 = 90,000.
(ii) 56802 → 57000 and 22475 → 22000.
Required sum = 57000 + 22000 = 79,000.
Estimate the following differences after rounding off each number to the nearest ten:
(i) 82 - 27
(ii) 96 - 36
(iii) 508 - 248
Answer
(i) 82 → 80 and 27 → 30.
Required difference = 80 - 30 = 50.
(ii) 96 → 100 and 36 → 40.
Required difference = 100 - 40 = 60.
(iii) 508 → 510 and 248 → 250.
Required difference = 510 - 250 = 260.
Estimate each difference after rounding off each given number to the nearest hundred:
(i) 769 - 314
(ii) 856 - 687
(iii) 6352 - 2086
Answer
(i) 769 → 800 and 314 → 300.
Required difference = 800 - 300 = 500.
(ii) 856 → 900 and 687 → 700.
Required difference = 900 - 700 = 200.
(iii) 6352 → 6400 and 2086 → 2100.
Required difference = 6400 - 2100 = 4300.
Estimate each difference after rounding off each given number to the nearest thousand:
(i) 45974 - 38766
(ii) 76003 - 48399
Answer
(i) 45974 → 46000 and 38766 → 39000.
Required difference = 46000 - 39000 = 7000.
(ii) 76003 → 76000 and 48399 → 48000.
Required difference = 76000 - 48000 = 28000.
Estimate each of the following products by rounding off each number to the nearest ten:
(i) 49 × 52
(ii) 63 × 38
(iii) 27 × 54
(iv) 53 × 85
(v) 74 × 67
(vi) 25 × 33
Answer
(i) 49 → 50 and 52 → 50.
Required product = 50 × 50 = 2500.
(ii) 63 → 60 and 38 → 40.
Required product = 60 × 40 = 2400.
(iii) 27 → 30 and 54 → 50.
Required product = 30 × 50 = 1500.
(iv) 53 → 50 and 85 → 90.
Required product = 50 × 90 = 4500.
(v) 74 → 70 and 67 → 70.
Required product = 70 × 70 = 4900.
(vi) 25 → 30 and 33 → 30.
Required product = 30 × 30 = 900.
Estimate each of the following products by rounding off each number to the nearest hundred:
(i) 477 × 213
(ii) 624 × 236
(iii) 333 × 247
(iv) 537 × 283
(v) 382 × 127
(vi) 472 × 328
Answer
(i) 477 → 500 and 213 → 200.
Required product = 500 × 200 = 1,00,000.
(ii) 624 → 600 and 236 → 200.
Required product = 600 × 200 = 1,20,000.
(iii) 333 → 300 and 247 → 200.
Required product = 300 × 200 = 60,000.
(iv) 537 → 500 and 283 → 300.
Required product = 500 × 300 = 1,50,000.
(v) 382 → 400 and 127 → 100.
Required product = 400 × 100 = 40,000.
(vi) 472 → 500 and 328 → 300.
Required product = 500 × 300 = 1,50,000.
Estimate each of the following products by rounding off the first number correct to the nearest ten and the other number correct to the nearest hundred:
(i) 28 × 287
(ii) 432 × 128
(iii) 48 × 165
(iv) 72 × 258
(v) 83 × 664
(vi) 44 × 250
Answer
(i) 28 → 30 (nearest ten) and 287 → 300 (nearest hundred).
Required product = 30 × 300 = 9000.
(ii) 432 → 430 (nearest ten) and 128 → 100 (nearest hundred).
Required product = 430 × 100 = 43000.
(iii) 48 → 50 (nearest ten) and 165 → 200 (nearest hundred).
Required product = 50 × 200 = 10000.
(iv) 72 → 70 (nearest ten) and 258 → 300 (nearest hundred).
Required product = 70 × 300 = 21000.
(v) 83 → 80 (nearest ten) and 664 → 700 (nearest hundred).
Required product = 80 × 700 = 56000.
(vi) 44 → 40 (nearest ten) and 250 → 300 (nearest hundred).
Required product = 40 × 300 = 12000.
Estimate each of the following quotients by rounding off 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
Answer
(i) 87 → 90 and 28 → 30.
Required quotient = = 3.
(ii) 84 → 80 and 23 → 20.
Required quotient = = 4.
(iii) 77 → 80 and 22 → 20.
Required quotient = = 4.
(iv) 198 → 200 and 24 → 20.
Required quotient = = 10.
(v) 355 → 360 and 26 → 30.
Required quotient = = 12.
(vi) 444 → 440 and 42 → 40.
Required quotient = = 11.
(vii) 843 → 840 and 33 → 30.
Required quotient = = 28.
There are 768 houses in a town and about 7 people live in each house. Round off these two numbers to the nearest ten and estimate the total number of people living in the town.
Answer
768 after rounding off to the nearest ten = 770
7 after rounding off to the nearest ten = 10
Estimated total number of people = 770 × 10 = 7,700
Hence, the estimated total number of people living in the town is 7,700.
There are 514 mango trees in an orchard. The owner plans to plant 178 more mango trees. Estimate how many mango trees will be there in the orchard after rounding off to the nearest hundred?
Answer
514 after rounding off to the nearest hundred = 500
178 after rounding off to the nearest hundred = 200
Estimated total number of mango trees = 500 + 200 = 700
Hence, there will be approximately 700 mango trees in the orchard.
A machine manufactures 5,782 screws every day. If we round off the number of screws produced in a day to the nearest thousand, approximately how many screws will the machine manufacture in the month of April?
Answer
5,782 after rounding off to the nearest thousand = 6,000
Number of days in the month of April = 30
Estimated number of screws manufactured = 6,000 × 30 = 1,80,000
Hence, the machine will manufacture approximately 1,80,000 screws in the month of April.
The weight of a box is 4 kg 859 g. What will be the approximate weight of 150 such boxes if we round off the weight of each box to 5 kg?
Answer
Weight of each box after rounding off = 5 kg
Estimated weight of 150 such boxes = 150 × 5 = 750 kg
Hence, the approximate weight of 150 boxes is 750 kg.