[discia] GCSE Maths › Number › Error Intervals

Error Intervals

discia.org 10 questions · 26 marks
Name Date
  1. Either paper 2 marks

    A garden cane is 79 cm long, correct to the nearest centimetre.

    Its length is \(x\) cm.

    Write down the error interval for \(x\).

    Show answer
    \(78.5 \leq x < 79.5\)
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  2. Either paper 2 marks

    1700 people went to a football match, correct to the nearest 100.

    (a)

    State the least possible number of people.

    (b)

    State the greatest possible number of people.

    Show answer
    (a) \(1650\)
    (b) \(1749\)
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  3. Either paper 2 marks

    A jug has a capacity of 5.8 litres, correct to 1 decimal place.

    The capacity is \(x\) litres.

    Write down the error interval for \(x\).

    Show answer
    \(5.75 \leq x < 5.85\)
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  4. Either paper 4 marks

    A garden hose is measured as 54 cm. Its true length is \(x\) cm.

    (a)

    The measurement has been rounded to the nearest centimetre.

    Write down the error interval for \(x\).

    (b)

    The measurement has instead been truncated to 54 cm.

    Write down the error interval for \(x\).

    Show answer
    (a) \(53.5 \leq x < 54.5\)
    (b) \(54 \leq x < 55\)
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  5. Either paper 4 marks

    The length of a plank is 4 metres, correct to the nearest metre.

    (a)

    Its length is \(l\) metres.

    Complete the error interval for the length of the plank.

    \(\underline{\phantom{00000}} \leq l < \underline{\phantom{00000}}\)

    (b)

    The length of a different plank is 11 metres, correct to the nearest metre.

    Joel says, "The total length of the two planks is 14 metres to the nearest metre."

    Give an example to show that Joel could be correct.

    Show answer
    (a) \(3.5 \leq l < 4.5\)
    (b) For example, lengths \(3.7\) m and \(10.6\) m: \(3.7 + 10.6 = 14.3\) m, which is 14 m to the nearest metre. (Any lengths with \(3.5 \leq\) first \(< 4.5\) and \(10.5 \leq\) second \(< 11.5\), whose total is from \(14\) up to but not including \(14.5\), are correct.)
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  6. Either paper 4 marks

    The length of a garden trellis is 290 cm, to the nearest 10 cm.

    (a)

    Its length is \(x\) cm.

    Complete the error interval for \(x\).

    (b)

    A different garden trellis measures 1.1 metres to the nearest 10 cm.

    Amara says that the total length of two of these garden trellises must be less than 2.31 m.

    Show that Amara is correct.

    Show answer
    (a) \(285 \leq x < 295\)
    (b) Upper bound 1.15 m, and \(2 \times 1.15 = 2.3\) m, which is less than 2.31 m, so Amara is correct
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  7. Either paper 2 marks

    The length of a rope is \(y\) m.

    When \(y\) is truncated to a whole number, the answer is 90.

    Omar writes the error interval due to truncation as

    \(89.5 \leq y < 90.5\)

    (a)

    Give a reason why Omar is wrong.

    (b)

    State the correct error interval for \(y\).

    Show answer
    (a) Omar has used the interval for rounding. Either reason earns the mark. Lower end: 89.5 is below 90, but truncation only cuts digits off, so \(y\) cannot be less than 90. Upper end: values from 90.5 up to 91 also truncate to 90 but are outside the rounding interval, so the upper end should be 91, not 90.5.
    (b) \(90 \leq y < 91\)
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  8. Either paper 2 marks

    A number \(n\) is 3100 correct to 2 significant figures.

    Write down the error interval for \(n\).

    Show answer
    \(3050 \leq n < 3150\)
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  9. Either paper 2 marks

    Callum used his calculator to work out the value of a number \(y\).

    The answer on his calculator display began 3.1

    Complete the error interval for \(y\).

    \(\ldots\ldots \leq y < \ldots\ldots\)

    Show answer
    \(3.1 \leq y < 3.2\)
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  10. Either paper 2 marks

    A steel cable is 64 cm long, correct to the nearest centimetre.

    Its length is \(x\) cm.

    Write down the error interval for \(x\).

    Show answer
    \(63.5 \leq x < 64.5\)
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discia.org Error Intervals · sheet 1
Answers Error Intervals · sheet 1
  1. \(78.5 \leq x < 79.5\)
  2. (a) \(1650\)
    (b) \(1749\)
  3. \(5.75 \leq x < 5.85\)
  4. (a) \(53.5 \leq x < 54.5\)
    (b) \(54 \leq x < 55\)
  5. (a) \(3.5 \leq l < 4.5\)
    (b) For example, lengths \(3.7\) m and \(10.6\) m: \(3.7 + 10.6 = 14.3\) m, which is 14 m to the nearest metre. (Any lengths with \(3.5 \leq\) first \(< 4.5\) and \(10.5 \leq\) second \(< 11.5\), whose total is from \(14\) up to but not including \(14.5\), are correct.)
  6. (a) \(285 \leq x < 295\)
    (b) Upper bound 1.15 m, and \(2 \times 1.15 = 2.3\) m, which is less than 2.31 m, so Amara is correct
  7. (a) Omar has used the interval for rounding. Either reason earns the mark. Lower end: 89.5 is below 90, but truncation only cuts digits off, so \(y\) cannot be less than 90. Upper end: values from 90.5 up to 91 also truncate to 90 but are outside the rounding interval, so the upper end should be 91, not 90.5.
    (b) \(90 \leq y < 91\)
  8. \(3050 \leq n < 3150\)
  9. \(3.1 \leq y < 3.2\)
  10. \(63.5 \leq x < 64.5\)
discia.org Error Intervals · sheet 1