Round each of the following numbers to the nearest ten :
(i) 54
(ii) 327
(iii) 2,793
(iv) 8,049
(v) 12,345
Answer
(i) 54
The units digit is 4. Since 4 is less than 5, we round down.
Hence, number rounded to the nearest ten = 50.
(ii) 327
The units digit is 7. Since 7 is 5 or greater, we round up the tens digit.
The tens digit (2) becomes 3, and the units digit becomes 0.
Hence, number rounded to the nearest ten = 330.
(iii) 2,793
The units digit is 3. Since 3 is less than 5, we round down.
Hence, number rounded to the nearest ten = 2,790.
(iv) 8,049
The units digit is 9. Since 9 is 5 or greater, we round up the tens digit.
The tens digit (4) becomes 5, and the units digit becomes 0.
Hence, number rounded to the nearest ten = 8,050.
(v) 12,345
The units digit is 5. Since 5 is 5 or greater, we round up the tens digit.
The tens digit (4) becomes 5, and the units digit becomes 0.
Hence, number rounded to the nearest ten = 12,350.
Round each of the following numbers to the nearest hundred :
(i) 925
(ii) 6,854
(iii) 41,263
(iv) 27,861
(v) 5,549
Answer
(i) 925
The tens digit is 2. Since 2 is less than 5, we round down.
The hundreds digit (9) remains the same, and the tens and units digits become 00.
Hence, number rounded to the nearest hundred = 900.
(ii) 6,854
The tens digit is 5. Since 5 is 5 or greater, we round up the hundreds digit.
The hundreds digit (8) becomes 9, and the tens and units digits become 00.
Hence, number rounded to the nearest hundred = 6,900.
(iii) 41,263
The tens digit is 6. Since 6 is 5 or greater, we round up the hundreds digit.
The hundreds digit (2) becomes 3, and the tens and units digits become 00.
Hence, number rounded to the nearest hundred = 41,300.
(iv) 27,861
The tens digit is 6. Since 6 is 5 or greater, we round up the hundreds digit.
The hundreds digit (8) becomes 9, and the tens and units digits become 00.
Hence, number rounded to the nearest hundred = 27,900.
(v) 5,549
The tens digit is 4. Since 4 is less than 5, we round down.
The hundreds digit (5) remains the same, and the tens and units digits become 00.
Hence, number rounded to the nearest hundred = 5,500.
Round each of the following numbers to the nearest thousand :
(i) 7,386
(ii) 34,276
(iii) 23,804
(iv) 76,540
Answer
(i) 7,386
The hundreds digit is 3. Since 3 is less than 5, we round down.
The thousands digit (7) remains the same, and the hundreds, tens, and units digits become 000.
Hence, number rounded to the nearest thousand = 7,000.
(ii) 34,276
The hundreds digit is 2. Since 2 is less than 5, we round down.
The thousands digit (4) remains the same, and the hundreds, tens, and units digits become 000.
Hence, number rounded to the nearest thousand = 34,000.
(iii) 23,804
The hundreds digit is 8. Since 8 is 5 or greater, we round up the thousands digit.
The thousands digit (3) becomes 4, and the hundreds, tens, and units digits become 000.
Hence, number rounded to the nearest thousand = 24,000.
(iv) 76,540
The hundreds digit is 5. Since 5 is 5 or greater, we round up the thousands digit.
The thousands digit (6) becomes 7, and the hundreds, tens, and units digits become 000.
Hence, number rounded to the nearest thousand = 77,000.
Find the approximate sum to the nearest ten :
(i) (72 + 37)
(ii) (264 + 348)
(iii) (2,538 + 6,274)
(iv) (4,782 + 2,345)
Answer
(i) (72 + 37)
Round 72 to the nearest ten: The units digit is 2, so it rounds down to 70.
Round 37 to the nearest ten: The units digit is 7, so it rounds up to 40.
Approximate sum: 70 + 40 = 110
Hence, the approximate sum = 110.
(ii) (264 + 348)
Round 264 to the nearest ten: The units digit is 4, so it rounds down to 260.
Round 348 to the nearest ten: The units digit is 8, so it rounds up to 350.
Approximate sum: 260 + 350 = 610
Hence, the approximate sum = 610.
(iii) (2,538 + 6,274)
Round 2,538 to the nearest ten: The units digit is 8, so it rounds up to 2,540.
Round 6,274 to the nearest ten: The units digit is 4, so it rounds down to 6,270.
Approximate sum: 2,540 + 6,270 = 8,810
Hence, the approximate sum = 8,810.
(iv) (4,782 + 2,345)
Round 4,782 to the nearest ten: The units digit is 2, so it rounds down to 4,780.
Round 2,345 to the nearest ten: The units digit is 5, so it rounds up to 2,350.
Approximate sum: 4,780 + 2,350 = 7,130
Hence, the approximate sum = 7,130.
Find the approximate sum to the nearest hundred :
(i) (347 + 476)
(ii) (654 + 247)
(iii) (5,240 + 3,421)
(iv) (9,483 + 6,572)
Answer
(i) (347 + 476)
Round 347 to the nearest hundred: The tens digit is 4, so it rounds down to 300.
Round 476 to the nearest hundred: The tens digit is 7, so it rounds up to 500.
Approximate sum: 300 + 500 = 800
Hence, the approximate sum = 800.
(ii) (654 + 247)
Round 654 to the nearest hundred: The tens digit is 5, so it rounds up to 700.
Round 247 to the nearest hundred: The tens digit is 4, so it rounds down to 200.
Approximate sum: 700 + 200 = 900
Hence, the approximate sum = 900.
(iii) (5,240 + 3,421)
Round 5,240 to the nearest hundred: The tens digit is 4, so it rounds down to 5,200.
Round 3,421 to the nearest hundred: The tens digit is 2, so it rounds down to 3,400.
Approximate sum: 5,200 + 3,400 = 8,600
Hence, the approximate sum = 8,600.
(iv) (9,483 + 6,572)
Round 9,483 to the nearest hundred: The tens digit is 8, so it rounds up to 9,500.
Round 6,572 to the nearest hundred: The tens digit is 7, so it rounds up to 6,600.
Approximate sum: 9,500 + 6,600 = 16,100
Hence, the approximate sum = 16,100.
Find the approximate sum to the nearest thousand :
(i) (43,728 + 36,275)
(ii) (37,804 + 22,475)
(iii) (6,785 + 2,476)
Answer
(i) (43,728 + 36,275)
Round 43,728 to the nearest thousand: The hundreds digit is 7, so it rounds up to 44,000.
Round 36,275 to the nearest thousand: The hundreds digit is 2, so it rounds down to 36,000.
Approximate sum: 44,000 + 36,000 = 80,000
Hence, the approximate sum = 80,000.
(ii) (37,804 + 22,475)
Round 37,804 to the nearest thousand: The hundreds digit is 8, so it rounds up to 38,000.
Round 22,475 to the nearest thousand: The hundreds digit is 4, so it rounds down to 22,000.
Approximate sum: 38,000 + 22,000 = 60,000
Hence, the approximate sum = 60,000.
(iii) (6,785 + 2,476)
Round 6,785 to the nearest thousand: The hundreds digit is 7, so it rounds up to 7,000.
Round 2,476 to the nearest thousand: The hundreds digit is 4, so it rounds down to 2,000.
Approximate sum: 7,000 + 2,000 = 9,000
Hence, the approximate sum = 9,000.
Find the approximate difference to the nearest ten :
(i) (64 - 29)
(ii) (186 - 49)
(iii) (429 - 206)
Answer
(i) Round 64 to the nearest ten: The units digit is 4, so it rounds down to 60.
Round 29 to the nearest ten: The units digit is 9, so it rounds up to 30.
Approximate difference: 60 − 30 = 30
Hence, the approximate difference = 30.
(ii) (186 − 49)
Round 186 to the nearest ten: The units digit is 6, so it rounds up to 190.
Round 49 to the nearest ten: The units digit is 9, so it rounds up to 50.
Approximate difference: 190 − 50 = 140
Hence, the approximate difference = 140.
(iii) (429 − 206)
Round 429 to the nearest ten: The units digit is 9, so it rounds up to 430.
Round 206 to the nearest ten: The units digit is 6, so it rounds up to 210.
Approximate difference: 430 − 210 = 220
Hence, the approximate difference = 220.
Find the approximate difference to the nearest hundred :
(i) (769 - 435)
(ii) (859 - 675)
(iii) (8,359 - 4,317)
Answer
(i) (769 - 435)
Round 769 to the nearest hundred: The tens digit is 6, so it rounds up to 800.
Round 435 to the nearest hundred: The tens digit is 3, so it rounds down to 400.
Approximate difference: 800 − 400 = 400
Hence, the approximate difference = 400.
(ii) (859 - 675)
Round 859 to the nearest hundred: The tens digit is 5, so it rounds up to 900.
Round 675 to the nearest hundred: The tens digit is 7, so it rounds up to 700.
Approximate difference: 900 − 700 = 200
Hence, the approximate difference = 200.
(iii) (8,359 - 4,317)
Round 8,359 to the nearest hundred: The tens digit is 5, so it rounds up to 8,400.
Round 4,317 to the nearest hundred: The tens digit is 1, so it rounds down to 4,300.
Approximate difference: 8,400 − 4,300 = 4,100
Hence, the approximate difference = 4,100.
Find the approximate difference to the nearest thousand :
(i) (45,783 - 38,695)
(ii) (38,005 - 29,375)
(iii) (7,654 - 4,368)
Answer
(i) (45,783 - 38,695)
Round 45,783 to the nearest thousand: The hundreds digit is 7, so it rounds up to 46,000.
Round 38,695 to the nearest thousand: The hundreds digit is 6, so it rounds up to 39,000.
Approximate difference: 46,000 − 39,000 = 7,000
Hence, the approximate difference = 7,000.
(ii) (38,005 - 29,375)
Round 38,005 to the nearest thousand: The hundreds digit is 0, so it rounds down to 38,000.
Round 29,375 to the nearest thousand: The hundreds digit is 3, so it rounds down to 29,000.
Approximate difference: 38,000 − 29,000 = 9,000
Hence, the approximate difference = 9,000.
(iii) (7,654 - 4,368)
Round 7,654 to the nearest thousand: The hundreds digit is 6, so it rounds up to 8,000.
Round 4,368 to the nearest thousand: The hundreds digit is 3, so it rounds down to 4,000.
Approximate difference: 8,000 − 4,000 = 4,000
Hence, the approximate difference = 4,000.
Estimate each of the following products by rounding off each number to the nearest ten:
(i) (49 × 72)
(ii) (39 × 62)
(iii) (63 × 57)
(iv) (35 × 43)
Answer
(i) (49 × 72)
Round 49 to the nearest ten: The units digit is 9, so it rounds up to 50.
Round 72 to the nearest ten: The units digit is 2, so it rounds down to 70.
Approximate product: 50 × 70 = 3,500
Hence, the approximate product = 3,500.
(ii) (39 × 62)
Round 39 to the nearest ten: The units digit is 9, so it rounds up to 40.
Round 62 to the nearest ten: The units digit is 2, so it rounds down to 60.
Approximate product: 40 × 60 = 2,400
Hence, the approximate product = 2,400.
(iii) (63 × 57)
Round 63 to the nearest ten: The units digit is 3, so it rounds down to 60.
Round 57 to the nearest ten: The units digit is 7, so it rounds up to 60.
Approximate product: 60 × 60 = 3,600
Hence, the approximate product = 3,600.
(iv) (35 × 43)
Round 35 to the nearest ten: The units digit is 5, so it rounds up to 40.
Round 43 to the nearest ten: The units digit is 3, so it rounds down to 40.
Approximate product: 40 × 40 = 1,600
Hence, the approximate product = 1,600.
Estimate each of the following products by rounding off each number to the nearest hundred :
(i) 265 × 334
(ii) 457 × 872
(iii) 381 × 316
(iv) 455 × 138
Answer
(i) 265 × 334
Round 265 to the nearest hundred: The tens digit is 6, so it rounds up to 300.
Round 334 to the nearest hundred: The tens digit is 3, so it rounds down to 300.
Approximate product: 300 × 300 = 90,000
Hence, the approximate product = 90,000.
(ii) 457 × 872
Round 457 to the nearest hundred: The tens digit is 5, so it rounds up to 500.
Round 872 to the nearest hundred: The tens digit is 7, so it rounds up to 900.
Approximate product: 500 × 900 = 4,50,000
Hence, the approximate product = 4,50,000.
(iii) 381 × 316
Round 381 to the nearest hundred: The tens digit is 8, so it rounds up to 400.
Round 316 to the nearest hundred: The tens digit is 1, so it rounds down to 300.
Approximate product: 400 × 300 = 1,20,000
Hence, the approximate product = 1,20,000.
(iv) 455 × 138
Round 455 to the nearest hundred: The tens digit is 5, so it rounds up to 500.
Round 138 to the nearest hundred: The tens digit is 3, so it rounds down to 100.
Approximate product: 500 × 100 = 50,000
Hence, the approximate product = 50,000.
Find the approximate quotient for each of the following :
(i) 86 ÷ 27
(ii) 83 ÷ 19
(iii) 286 ÷ 25
(iv) 865 ÷ 38
Answer
(i) 86 ÷ 27
Round 86 to the nearest ten: 90
Round 27 to the nearest ten: 30
Approximate quotient: 90 ÷ 30 = 3
Hence, the approximate quotient = 3.
(ii) 83 ÷ 19
Round 83 to the nearest ten: 80
Round 19 to the nearest ten: 20
Approximate quotient: 80 ÷ 20 = 4
Hence, the approximate quotient = 4.
(iii) 286 ÷ 25
Round 286 to the nearest hundred: 300
Round 25 to the nearest ten: 30
Approximate quotient: 300 ÷ 30 = 10
Hence, the approximate quotient = 10.
(iv) 865 ÷ 38
Round 865 to the nearest hundred: 900
Round 38 to the nearest ten: 40
Approximate quotient: 900 ÷ 40 = 90 ÷ 4 = 22.5.
Since we are looking for an approximate quotient, we can round to the nearest whole number.
Approximate quotient: 23
Hence, the approximate quotient = 23.