[discia] GCSE Maths › Number › Estimating

Estimating

discia.org 10 questions · 27 marks
Name Date
  1. Non-calculator 2 marks

    Estimate the value of \(73.3 \times 8.3\).

    Round each number to 1 significant figure.

    Show answer
    \(560\)
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  2. Non-calculator 3 marks

    Three warehouses hold these numbers of boxes.

    \(2,347\), \(3,180\), \(5,946\)

    (a)

    Work out an estimate of the total, by rounding each number to the nearest 1000.

    (b)

    Is your estimate bigger or smaller than the exact total?

    Give a reason for your answer.

    Show answer
    (a) \(11000\)
    (b) Smaller — the exact total is 11,473, so the estimate is out by 473.
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  3. Non-calculator 3 marks

    Tomas tries to work out \(\frac{ 87.87 + 69.63 }{ 14.07 }\).

    He writes down the answer \(92.82\).

    By rounding each number to the nearest 10, show that his answer is incorrect.

    Show answer
    Estimate \(\frac{ 90 + 70 }{10} = 16\); Tomas wrote \(92.82\), which is far from \(16\), so the answer is incorrect.
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  4. Non-calculator 3 marks

    Estimate the value of \(\frac{ 76.8 \times 64.8 }{ 5.1 }\).

    Round each number to 1 significant figure.

    Show answer
    \(960\)
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  5. Non-calculator 3 marks

    Work out an estimate for the value of \(\sqrt{ 28.3 \times 29.5 }\).

    Round each number to 1 significant figure.

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    \(30\)
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  6. Non-calculator 3 marks

    A school buys 54 calculators costing £6.20 each.

    (a)

    Work out an estimate for the total cost. Round each number to 1 significant figure.

    (b)

    Is your estimate an over-estimate or an under-estimate of the true cost? Give a reason for your answer.

    Show answer
    (a) \(\text{£}300\)
    (b) An under-estimate
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  7. Non-calculator 3 marks

    A stadium holds 3106 people.

    Find an estimate of 41% of 3106.

    You must show your working.

    Show answer
    \(1200\ \text{people}\)
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  8. Non-calculator 2 marks

    A roll of ribbon is 71.19 m long.

    It is to be cut into pieces that are each 0.69 m long.

    Calculate an estimate of how many pieces can be cut from the roll.

    You must show your working.

    Show answer
    \(100\)
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  9. Non-calculator 3 marks

    Nadia uses a calculator to work out \(63.6 \times 24\).

    She writes down the answer \(152640\).

    (a)

    Calculate an estimate of \(63.6 \times 24\) by rounding each number to 1 significant figure.

    (b)

    Explain how your estimate shows that Nadia's answer is wrong.

    Show answer
    (a) \(1200\)
    (b) The estimate is about 1200, but Nadia wrote \(152640\), which is far bigger than that.
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  10. Non-calculator 2 marks

    An office buys 45 printers for a total of £1953.00.

    Calculate an estimate of the cost of one printer.

    You must show your working.

    Show answer
    \(\text{£}40\)
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discia.org Estimating · sheet 1
Answers Estimating · sheet 1
  1. \(560\)
  2. (a) \(11000\)
    (b) Smaller — the exact total is 11,473, so the estimate is out by 473.
  3. Estimate \(\frac{ 90 + 70 }{10} = 16\); Tomas wrote \(92.82\), which is far from \(16\), so the answer is incorrect.
  4. \(960\)
  5. \(30\)
  6. (a) \(\text{£}300\)
    (b) An under-estimate
  7. \(1200\ \text{people}\)
  8. \(100\)
  9. (a) \(1200\)
    (b) The estimate is about 1200, but Nadia wrote \(152640\), which is far bigger than that.
  10. \(\text{£}40\)
discia.org Estimating · sheet 1