# 數學題[10分]

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 58 mm(correct to the nearest mm) and then dividing his measured value by the totoal number of pieces of paper.

(1)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%

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

Rating

(1)Find

(i)the maximum error of the thickness of a piece of paper

As the thickness for 500 pieces is correct to the nearest mm

so the maximum error of the thickness of 500 pieces of paper is 0.5mm

hence the maximum error of the thickness of a piece of paper is

error of total number of paper / number of paper

= 0.5/500

= 0.001 mm

(ii)the thickness of each piece of paper

58/500 = 0.116

so the thickness of each piece of paper is 0.116mm

(iii)the percentage error,correct to the nearest 0.1%

the percentage error = error/measurement *100% = 0.001/0.116 * 100%

= 0.862%

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

when less pieces of paper is used, as the measurement error remain unchange = 0.5mm

the error for a piece of paper =

error of total number of paper / number of paper

will then increase.

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Source(s): 自己既計算