小芝芝 asked in 科學及數學數學 · 1 decade ago

S2 Math

Please help me to solve the following questions.

1. The time taken by an athlete to finish a long distance race is measured to

be 1h 24min 13s and the error is at most 1s.

What is the percentage error of this measurement?

(give the answer correct to the nearest 0.01%0

2. The height of the Buddha statue on Lantau Island is measured to be

26.4m and the percentage error is 25/33%. Find the range of the

actual height.

3. Charles wants to know the thickness of a piece of paper by first measuring

the thickness of a pile of 500 pieces of paper to be 58mm (correct to the

nearest mm) and then dividing his measured value by the total number of

pieces of paper.

(a) Find i]the maximum error of the thickness of a piece of paper;

ii] the thickness of each piece of paper;

iii] the percentage error, correct to the nearest 0.1%

(b) Will he get a larger or smaller error ir he uses less pieces of paper?

Thank You for helping.

1 Answer

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  • 1 decade ago
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    1. The time taken by an athlete to finish a long distance race is measured to

    be 1h 24min 13s and the error is at most 1s.

    What is the percentage error of this measurement?

    (give the answer correct to the nearest 0.01%)

    A. the percentage error

    = 1s/[(60+24)60+13]s*100%

    (= 0.019790223%)-------------not necessary for writing this line

    = 0.02%

    2. The height of the Buddha statue on Lantau Island is measured to be

    26.4m and the percentage error is 25/33%. Find the range of the

    actual height.

    A. Let y m be the maximum absolute error.

    y/26.4*100% = 25/33%

    y = 25/33%*26.4

    y = 0.2

    Therefore the maximum absolute error is 0.2 m.

    The upper limit = (26.4-0.2)m = 26.2m

    The lower limit = (26.4+0.2)m = 26.6m

    Therefore the range is between 26.2m to 26.6m.

    3. Charles wants to know the thickness of a piece of paper by first measuring

    the thickness of a pile of 500 pieces of paper to be 58mm (correct to the

    nearest mm) and then dividing his measured value by the total number of

    pieces of paper.

    (a) Find

    i] the maximum error of the thickness of a piece of paper;

    A. the maximum absolute error

    = (1mm/2)/500

    = 0.5mm/500

    = 0.001mm

    ii] the thickness of each piece of paper;

    A. the thickness

    = 58mm/500

    = 0.116mm

    iii] the percentage error, correct to the nearest 0.1%

    A. the percentage error

    = 0.001mm/0.116mm*100%

    = 0.9%

    (b) Will he get a larger or smaller error if he uses less pieces of paper?

    A. Sorry, I don’t know what the answer is.

    2010-12-03 20:12:50 補充:

    Thanks for STH.

    Q.2: the upper limit and lower limit should be interchanged

    Source(s): Myself
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