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 1 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 283.1 to round to the 1 significant figure

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

    The next digit is 8, which is 5 or more, so we round up.

  2. Round 283.1

    283.1≈300283.1 \approx 300

    283.1 rounds to 300.

  3. Look at 787.1 to round to the 1 significant figure

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

    The next digit is 8, which is 5 or more, so we round up.

  4. Round 787.1

    787.1≈800787.1 \approx 800

    787.1 rounds to 800.

  5. Look at 752.0 to round to the 1 significant figure

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

    The next digit is 5, which is 5 or more, so we round up.

  6. Round 752.0

    752.0≈800752.0 \approx 800

    752.0 rounds to 800.

  7. Look at 536.2 to round to the 1 significant figure

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

    The next digit is 3, which is less than 5, so we round down.

  8. Round 536.2

    536.2≈500536.2 \approx 500

    536.2 rounds to 500.

  9. Look at 456.8 to round to the 1 significant figure

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

    The next digit is 5, which is 5 or more, so we round up.

  10. Round 456.8

    456.8≈500456.8 \approx 500

    456.8 rounds to 500.

  11. Look at 68.2 to round to the 1 significant figure

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

    The next digit is 8, which is 5 or more, so we round up.

  12. Round 68.2

    68.2≈7068.2 \approx 70

    68.2 rounds to 70.

  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 2970.

Answer
29702970
Question 2
6 markschallenging
A school orders supplies for six departments. By rounding each value to the nearest 100, estimate the total of 45364536, 34943494, 621621, 291291, 53585358, 11541154.
Show worked solution

Worked solution

  1. Look at 4536 to round to the nearest 100

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

    The next digit is 3, which is less than 5, so we round down.

  2. Round 4536

    4536≈45004536 \approx 4500

    4536 rounds to 4500.

  3. Look at 3494 to round to the nearest 100

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

    The next digit is 9, which is 5 or more, so we round up.

  4. Round 3494

    3494≈35003494 \approx 3500

    3494 rounds to 3500.

  5. Look at 621 to round to the nearest 100

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

    The next digit is 2, which is less than 5, so we round down.

  6. Round 621

    621≈600621 \approx 600

    621 rounds to 600.

  7. Look at 291 to round to the nearest 100

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

    The next digit is 9, which is 5 or more, so we round up.

  8. Round 291

    291≈300291 \approx 300

    291 rounds to 300.

  9. Look at 5358 to round to the nearest 100

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

    The next digit is 5, which is 5 or more, so we round up.

  10. Round 5358

    5358≈54005358 \approx 5400

    5358 rounds to 5400.

  11. Look at 1154 to round to the nearest 100

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

    The next digit is 5, which is 5 or more, so we round up.

  12. Round 1154

    1154≈12001154 \approx 1200

    1154 rounds to 1200.

  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 15500.

Answer
1550015500
Question 3
5 markschallenging
A factory logs six daily outputs. By rounding each value to the nearest 10, estimate the total of 3333, 2929, 9696, 154154, 7171, 164164.
Show worked solution

Worked solution

  1. Look at 33 to round to the nearest 10

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

    The next digit is 3, which is less than 5, so we round down.

  2. Round 33

    33≈3033 \approx 30

    33 rounds to 30.

  3. Look at 29 to round to the nearest 10

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

    The next digit is 9, which is 5 or more, so we round up.

  4. Round 29

    29≈3029 \approx 30

    29 rounds to 30.

  5. Look at 96 to round to the nearest 10

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

    The next digit is 6, which is 5 or more, so we round up.

  6. Round 96

    96≈10096 \approx 100

    96 rounds to 100.

  7. Look at 154 to round to the nearest 10

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

    The next digit is 4, which is less than 5, so we round down.

  8. Round 154

    154≈150154 \approx 150

    154 rounds to 150.

  9. Look at 71 to round to the nearest 10

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

    The next digit is 1, which is less than 5, so we round down.

  10. Round 71

    71≈7071 \approx 70

    71 rounds to 70.

  11. Look at 164 to round to the nearest 10

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

    The next digit is 4, which is less than 5, so we round down.

  12. Round 164

    164≈160164 \approx 160

    164 rounds to 160.

  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 540.

Answer
540540
Question 4
6 markschallenging
Six fields are measured. By rounding each value to the 1 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 838.8 to round to the 1 significant figure

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

    The next digit is 3, which is less than 5, so we round down.

  2. Round 838.8

    838.8≈800838.8 \approx 800

    838.8 rounds to 800.

  3. Look at 586.8 to round to the 1 significant figure

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

    The next digit is 8, which is 5 or more, so we round up.

  4. Round 586.8

    586.8≈600586.8 \approx 600

    586.8 rounds to 600.

  5. Look at 695.8 to round to the 1 significant figure

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

    The next digit is 9, which is 5 or more, so we round up.

  6. Round 695.8

    695.8≈700695.8 \approx 700

    695.8 rounds to 700.

  7. Look at 651.3 to round to the 1 significant figure

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

    The next digit is 5, which is 5 or more, so we round up.

  8. Round 651.3

    651.3≈700651.3 \approx 700

    651.3 rounds to 700.

  9. Look at 886.6 to round to the 1 significant figure

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

    The next digit is 8, which is 5 or more, so we round up.

  10. Round 886.6

    886.6≈900886.6 \approx 900

    886.6 rounds to 900.

  11. Look at 279.1 to round to the 1 significant figure

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

    The next digit is 7, which is 5 or more, so we round up.

  12. Round 279.1

    279.1≈300279.1 \approx 300

    279.1 rounds to 300.

  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 4000.

Answer
40004000
Question 5
5 markschallenging
A charity records six donations. By rounding each value to the nearest 100, estimate the total of 39233923, 13001300, 16191619, 32263226, 40294029, 18931893.
Show worked solution

Worked solution

  1. Look at 3923 to round to the nearest 100

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

    The next digit is 2, which is less than 5, so we round down.

  2. Round 3923

    3923≈39003923 \approx 3900

    3923 rounds to 3900.

  3. Look at 1300 to round to the nearest 100

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

    The next digit is 0, which is less than 5, so we round down.

  4. Round 1300

    1300≈13001300 \approx 1300

    1300 rounds to 1300.

  5. Look at 1619 to round to the nearest 100

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

    The next digit is 1, which is less than 5, so we round down.

  6. Round 1619

    1619≈16001619 \approx 1600

    1619 rounds to 1600.

  7. Look at 3226 to round to the nearest 100

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

    The next digit is 2, which is less than 5, so we round down.

  8. Round 3226

    3226≈32003226 \approx 3200

    3226 rounds to 3200.

  9. Look at 4029 to round to the nearest 100

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

    The next digit is 2, which is less than 5, so we round down.

  10. Round 4029

    4029≈40004029 \approx 4000

    4029 rounds to 4000.

  11. Look at 1893 to round to the nearest 100

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

    The next digit is 9, which is 5 or more, so we round up.

  12. Round 1893

    1893≈19001893 \approx 1900

    1893 rounds to 1900.

  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 15900.

Answer
1590015900

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