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1) By using a stop-watch,Peter finds that the time taken for a colour printer to print 100 identical documents is 7 minutes 5 seconds, and the relative error is 1/85.what is the possible range of time required to print 1 document?2)The maximum pulling strength of a fishing-line measured by a laboratory is... 顯示更多 1) By using a stop-watch,Peter finds that the time taken for a colour printer to print 100 identical documents is 7 minutes 5 seconds, and the relative error is 1/85.what is the possible range of time required to print 1 document? 2)The maximum pulling strength of a fishing-line measured by a laboratory is 60kg and the percentage error is 5%. What is the possible range of the maximum pulling strength of the fishing-line? 3)The time required for an anti-virus software to scan all the files of computer is measured by a programmer to be 19 minuts 15 seconds, correct to the nearest 5 seconds.FRind the percentage error of the measured time correct to 2 sig.fig. 4)An observatory records that the Leo meteor shower appears every 33 years, correct to the nearest 0.5 year,and the Halley's comet returns every every 76 years, correct to the nearest year. (a)Find the percentage error for each of these recorded time, correct to 2 sig. fig. (b)Compare the two recorded time to find out which one is more accurate.
最佳解答:
1) 7 minutes 5 seconds = (7x60 + 5)sec = 425 seconds lower limit = (100 - 100 x 1/85)/100 = 0.9882 (corr to 4 decimal place) upper limit = (100 + 100 x 1/85)/100 = 1.0118 (corr to 4 decimal place) Therefore, the possible range of time required to print 1 documnet is 0.9882 to 1.0118 2) The upper limit = 60kg x (1+5%) = 60kg x 1.05 = 63kg The lower limit = 60kg x (1- 5%) = 60kg x 0.95 = 57kg Therefore the possible range of the maximum pulling strength of the fishing-ine is 57kg - 63kg 3) 19 min 15 sec = (19 x 60 + 15) seconds = 1155 seconds The percentage error of the measured time is: 5 / 1155 x 100% = 0.43% (corr to 2 sig.fig.) 4a) The percentage error of Leo meteor shower recoreded time: 0.5 / 33 x 100% = 1.5% (corr to 2 sig. fig.) The percentage error of Halley's comet recorded time: 1 / 76 x 100% = 1.3% (corr to 2 sig. fig.) 4b) From the answer 4a, the percentage error of Halley's comet recorded time is smaller than that of leo meteor shower, therefore Halley's comet is more accurate
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S.2-S.3 Maths(Approximation and errors)發問:
1) By using a stop-watch,Peter finds that the time taken for a colour printer to print 100 identical documents is 7 minutes 5 seconds, and the relative error is 1/85.what is the possible range of time required to print 1 document?2)The maximum pulling strength of a fishing-line measured by a laboratory is... 顯示更多 1) By using a stop-watch,Peter finds that the time taken for a colour printer to print 100 identical documents is 7 minutes 5 seconds, and the relative error is 1/85.what is the possible range of time required to print 1 document? 2)The maximum pulling strength of a fishing-line measured by a laboratory is 60kg and the percentage error is 5%. What is the possible range of the maximum pulling strength of the fishing-line? 3)The time required for an anti-virus software to scan all the files of computer is measured by a programmer to be 19 minuts 15 seconds, correct to the nearest 5 seconds.FRind the percentage error of the measured time correct to 2 sig.fig. 4)An observatory records that the Leo meteor shower appears every 33 years, correct to the nearest 0.5 year,and the Halley's comet returns every every 76 years, correct to the nearest year. (a)Find the percentage error for each of these recorded time, correct to 2 sig. fig. (b)Compare the two recorded time to find out which one is more accurate.
最佳解答:
1) 7 minutes 5 seconds = (7x60 + 5)sec = 425 seconds lower limit = (100 - 100 x 1/85)/100 = 0.9882 (corr to 4 decimal place) upper limit = (100 + 100 x 1/85)/100 = 1.0118 (corr to 4 decimal place) Therefore, the possible range of time required to print 1 documnet is 0.9882 to 1.0118 2) The upper limit = 60kg x (1+5%) = 60kg x 1.05 = 63kg The lower limit = 60kg x (1- 5%) = 60kg x 0.95 = 57kg Therefore the possible range of the maximum pulling strength of the fishing-ine is 57kg - 63kg 3) 19 min 15 sec = (19 x 60 + 15) seconds = 1155 seconds The percentage error of the measured time is: 5 / 1155 x 100% = 0.43% (corr to 2 sig.fig.) 4a) The percentage error of Leo meteor shower recoreded time: 0.5 / 33 x 100% = 1.5% (corr to 2 sig. fig.) The percentage error of Halley's comet recorded time: 1 / 76 x 100% = 1.3% (corr to 2 sig. fig.) 4b) From the answer 4a, the percentage error of Halley's comet recorded time is smaller than that of leo meteor shower, therefore Halley's comet is more accurate
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