Hard GCSE Rounding Questions

Challenging, exam-style GCSE Rounding questions with worked solutions. Stretch yourself on the hardest rounding, estimation, nearest, sf problems.

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GCSE Foundation34 questionsStep-by-step solutions
Question 1
5 markschallenging
Six stages of a race are timed. By rounding each value to the 11 significant figure, estimate the total of 283.1283.1, 787.1787.1, 752.0752.0, 536.2536.2, 456.8456.8, 68.268.2.
Show worked solution

Worked solution

  1. Look at 283.1283.1 to round to the 11 significant figure

    283.1 (deciding digit 8)283.1\ (\text{deciding digit } 8)

    The next digit is 88, which is 55 or more, so we round up.

  2. Round 283.1283.1

    283.1300283.1 \approx 300

    283.1283.1 rounds to 300300.

  3. Look at 787.1787.1 to round to the 11 significant figure

    787.1 (deciding digit 8)787.1\ (\text{deciding digit } 8)

    The next digit is 88, which is 55 or more, so we round up.

  4. Round 787.1787.1

    787.1800787.1 \approx 800

    787.1787.1 rounds to 800800.

  5. Look at 752.0752.0 to round to the 11 significant figure

    752.0 (deciding digit 5)752.0\ (\text{deciding digit } 5)

    The next digit is 55, which is 55 or more, so we round up.

  6. Round 752.0752.0

    752.0800752.0 \approx 800

    752.0752.0 rounds to 800800.

  7. Look at 536.2536.2 to round to the 11 significant figure

    536.2 (deciding digit 3)536.2\ (\text{deciding digit } 3)

    The next digit is 33, which is less than 55, so we round down.

  8. Round 536.2536.2

    536.2500536.2 \approx 500

    536.2536.2 rounds to 500500.

  9. Look at 456.8456.8 to round to the 11 significant figure

    456.8 (deciding digit 5)456.8\ (\text{deciding digit } 5)

    The next digit is 55, which is 55 or more, so we round up.

  10. Round 456.8456.8

    456.8500456.8 \approx 500

    456.8456.8 rounds to 500500.

  11. Look at 68.268.2 to round to the 11 significant figure

    68.2 (deciding digit 8)68.2\ (\text{deciding digit } 8)

    The next digit is 88, which is 55 or more, so we round up.

  12. Round 68.268.2

    68.27068.2 \approx 70

    68.268.2 rounds to 7070.

  13. Add the first group of rounded values

    300+800+800=1900300 + 800 + 800 = 1900

    Add the first half of the rounded numbers.

  14. Add the second group of rounded values

    500+500+70=1070500 + 500 + 70 = 1070

    Add the second half of the rounded numbers.

  15. Combine the two subtotals

    1900+1070=29701900 + 1070 = 2970

    The estimated total is 29702970.

Answer
29702970
Question 2
6 markschallenging
A school orders supplies for six departments. By rounding each value to the nearest 100100, estimate the total of 45364536, 34943494, 621621, 291291, 53585358, 11541154.
Show worked solution

Worked solution

  1. Look at 45364536 to round to the nearest 100100

    4536 (deciding digit 3)4536\ (\text{deciding digit } 3)

    The next digit is 33, which is less than 55, so we round down.

  2. Round 45364536

    453645004536 \approx 4500

    45364536 rounds to 45004500.

  3. Look at 34943494 to round to the nearest 100100

    3494 (deciding digit 9)3494\ (\text{deciding digit } 9)

    The next digit is 99, which is 55 or more, so we round up.

  4. Round 34943494

    349435003494 \approx 3500

    34943494 rounds to 35003500.

  5. Look at 621621 to round to the nearest 100100

    621 (deciding digit 2)621\ (\text{deciding digit } 2)

    The next digit is 22, which is less than 55, so we round down.

  6. Round 621621

    621600621 \approx 600

    621621 rounds to 600600.

  7. Look at 291291 to round to the nearest 100100

    291 (deciding digit 9)291\ (\text{deciding digit } 9)

    The next digit is 99, which is 55 or more, so we round up.

  8. Round 291291

    291300291 \approx 300

    291291 rounds to 300300.

  9. Look at 53585358 to round to the nearest 100100

    5358 (deciding digit 5)5358\ (\text{deciding digit } 5)

    The next digit is 55, which is 55 or more, so we round up.

  10. Round 53585358

    535854005358 \approx 5400

    53585358 rounds to 54005400.

  11. Look at 11541154 to round to the nearest 100100

    1154 (deciding digit 5)1154\ (\text{deciding digit } 5)

    The next digit is 55, which is 55 or more, so we round up.

  12. Round 11541154

    115412001154 \approx 1200

    11541154 rounds to 12001200.

  13. Add the first group of rounded values

    4500+3500+600=86004500 + 3500 + 600 = 8600

    Add the first half of the rounded numbers.

  14. Add the second group of rounded values

    300+5400+1200=6900300 + 5400 + 1200 = 6900

    Add the second half of the rounded numbers.

  15. Combine the two subtotals

    8600+6900=155008600 + 6900 = 15500

    The estimated total is 1550015500.

Answer
1550015500
Question 3
5 markschallenging
A factory logs six daily outputs. By rounding each value to the nearest 1010, estimate the total of 3333, 2929, 9696, 154154, 7171, 164164.
Show worked solution

Worked solution

  1. Look at 3333 to round to the nearest 1010

    33 (deciding digit 3)33\ (\text{deciding digit } 3)

    The next digit is 33, which is less than 55, so we round down.

  2. Round 3333

    333033 \approx 30

    3333 rounds to 3030.

  3. Look at 2929 to round to the nearest 1010

    29 (deciding digit 9)29\ (\text{deciding digit } 9)

    The next digit is 99, which is 55 or more, so we round up.

  4. Round 2929

    293029 \approx 30

    2929 rounds to 3030.

  5. Look at 9696 to round to the nearest 1010

    96 (deciding digit 6)96\ (\text{deciding digit } 6)

    The next digit is 66, which is 55 or more, so we round up.

  6. Round 9696

    9610096 \approx 100

    9696 rounds to 100100.

  7. Look at 154154 to round to the nearest 1010

    154 (deciding digit 4)154\ (\text{deciding digit } 4)

    The next digit is 44, which is less than 55, so we round down.

  8. Round 154154

    154150154 \approx 150

    154154 rounds to 150150.

  9. Look at 7171 to round to the nearest 1010

    71 (deciding digit 1)71\ (\text{deciding digit } 1)

    The next digit is 11, which is less than 55, so we round down.

  10. Round 7171

    717071 \approx 70

    7171 rounds to 7070.

  11. Look at 164164 to round to the nearest 1010

    164 (deciding digit 4)164\ (\text{deciding digit } 4)

    The next digit is 44, which is less than 55, so we round down.

  12. Round 164164

    164160164 \approx 160

    164164 rounds to 160160.

  13. Add the first group of rounded values

    30+30+100=16030 + 30 + 100 = 160

    Add the first half of the rounded numbers.

  14. Add the second group of rounded values

    150+70+160=380150 + 70 + 160 = 380

    Add the second half of the rounded numbers.

  15. Combine the two subtotals

    160+380=540160 + 380 = 540

    The estimated total is 540540.

Answer
540540
Question 4
6 markschallenging
Six fields are measured. By rounding each value to the 11 significant figure, estimate the total of 838.8838.8, 586.8586.8, 695.8695.8, 651.3651.3, 886.6886.6, 279.1279.1.
Show worked solution

Worked solution

  1. Look at 838.8838.8 to round to the 11 significant figure

    838.8 (deciding digit 3)838.8\ (\text{deciding digit } 3)

    The next digit is 33, which is less than 55, so we round down.

  2. Round 838.8838.8

    838.8800838.8 \approx 800

    838.8838.8 rounds to 800800.

  3. Look at 586.8586.8 to round to the 11 significant figure

    586.8 (deciding digit 8)586.8\ (\text{deciding digit } 8)

    The next digit is 88, which is 55 or more, so we round up.

  4. Round 586.8586.8

    586.8600586.8 \approx 600

    586.8586.8 rounds to 600600.

  5. Look at 695.8695.8 to round to the 11 significant figure

    695.8 (deciding digit 9)695.8\ (\text{deciding digit } 9)

    The next digit is 99, which is 55 or more, so we round up.

  6. Round 695.8695.8

    695.8700695.8 \approx 700

    695.8695.8 rounds to 700700.

  7. Look at 651.3651.3 to round to the 11 significant figure

    651.3 (deciding digit 5)651.3\ (\text{deciding digit } 5)

    The next digit is 55, which is 55 or more, so we round up.

  8. Round 651.3651.3

    651.3700651.3 \approx 700

    651.3651.3 rounds to 700700.

  9. Look at 886.6886.6 to round to the 11 significant figure

    886.6 (deciding digit 8)886.6\ (\text{deciding digit } 8)

    The next digit is 88, which is 55 or more, so we round up.

  10. Round 886.6886.6

    886.6900886.6 \approx 900

    886.6886.6 rounds to 900900.

  11. Look at 279.1279.1 to round to the 11 significant figure

    279.1 (deciding digit 7)279.1\ (\text{deciding digit } 7)

    The next digit is 77, which is 55 or more, so we round up.

  12. Round 279.1279.1

    279.1300279.1 \approx 300

    279.1279.1 rounds to 300300.

  13. Add the first group of rounded values

    800+600+700=2100800 + 600 + 700 = 2100

    Add the first half of the rounded numbers.

  14. Add the second group of rounded values

    700+900+300=1900700 + 900 + 300 = 1900

    Add the second half of the rounded numbers.

  15. Combine the two subtotals

    2100+1900=40002100 + 1900 = 4000

    The estimated total is 40004000.

Answer
40004000
Question 5
5 markschallenging
A charity records six donations. By rounding each value to the nearest 100100, estimate the total of 39233923, 13001300, 16191619, 32263226, 40294029, 18931893.
Show worked solution

Worked solution

  1. Look at 39233923 to round to the nearest 100100

    3923 (deciding digit 2)3923\ (\text{deciding digit } 2)

    The next digit is 22, which is less than 55, so we round down.

  2. Round 39233923

    392339003923 \approx 3900

    39233923 rounds to 39003900.

  3. Look at 13001300 to round to the nearest 100100

    1300 (deciding digit 0)1300\ (\text{deciding digit } 0)

    The next digit is 00, which is less than 55, so we round down.

  4. Round 13001300

    130013001300 \approx 1300

    13001300 rounds to 13001300.

  5. Look at 16191619 to round to the nearest 100100

    1619 (deciding digit 1)1619\ (\text{deciding digit } 1)

    The next digit is 11, which is less than 55, so we round down.

  6. Round 16191619

    161916001619 \approx 1600

    16191619 rounds to 16001600.

  7. Look at 32263226 to round to the nearest 100100

    3226 (deciding digit 2)3226\ (\text{deciding digit } 2)

    The next digit is 22, which is less than 55, so we round down.

  8. Round 32263226

    322632003226 \approx 3200

    32263226 rounds to 32003200.

  9. Look at 40294029 to round to the nearest 100100

    4029 (deciding digit 2)4029\ (\text{deciding digit } 2)

    The next digit is 22, which is less than 55, so we round down.

  10. Round 40294029

    402940004029 \approx 4000

    40294029 rounds to 40004000.

  11. Look at 18931893 to round to the nearest 100100

    1893 (deciding digit 9)1893\ (\text{deciding digit } 9)

    The next digit is 99, which is 55 or more, so we round up.

  12. Round 18931893

    189319001893 \approx 1900

    18931893 rounds to 19001900.

  13. Add the first group of rounded values

    3900+1300+1600=68003900 + 1300 + 1600 = 6800

    Add the first half of the rounded numbers.

  14. Add the second group of rounded values

    3200+4000+1900=91003200 + 4000 + 1900 = 9100

    Add the second half of the rounded numbers.

  15. Combine the two subtotals

    6800+9100=159006800 + 9100 = 15900

    The estimated total is 1590015900.

Answer
1590015900

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