S2 Math

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