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標題:
Maths!!!
發問:
Leo uses a ruler on which the distance between 2 successive markings is 5 mm to measure the sides of a rectangle and here are the result: Length =4.5cm Width=6.5cm If he uses the measured lengths to calculate the area of the rectagle,find the accumulated error in the result obtained.
最佳解答:
其他解答:
Maths!!!
發問:
Leo uses a ruler on which the distance between 2 successive markings is 5 mm to measure the sides of a rectangle and here are the result: Length =4.5cm Width=6.5cm If he uses the measured lengths to calculate the area of the rectagle,find the accumulated error in the result obtained.
最佳解答:
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Distance between 2 successive markings = 5mm So, the sides of the rectangle are correct to the nearest 5mm Maximum absolute error = 5mm / 2 = 2.5 mm = 0.25 cm ( 4.5 - 0.25 )cm <= Length < ( 4.5 + 0.25 ) cm 4.25 cm <= Length < 4.75 cm You may ask why the former sign is <= but the latter one is < It is because if the real length is 4.75cm, it lies exactly in the middle of 4.5cm and 5cm. 佢會四捨五入左變 5cm. Therefore, if it is measured to be 4.5 cm, the exact length cannot be 4.75 cm. If the real length is 4.25 cm, it lies exactly in the middle of 4cm and 4.25cm. For the same reason, it will be taken as 4.5 cm. Therefore, if it is measured to be 4.5 cm, the exact length can be 4.25 cm. ( 6.5 - 0.25 )cm <= Width < ( 6.5 + 0.25 )cm 6.25 cm <= Width < 6.75 cm Minimum area of rectangle = 4.25 x 6.25 = 26.5625 cm2 ........................ ( 1 ) Maximum area of rectangle = 4.75 x 6.75 = 32.0625 cm2 ........................ ( 2 ) Area of rectangle of measured sides are used = 4.5 x 6.5 = 29.25 cm2 .............................. ( 3 ) ( 3 ) - ( 1 ) = 29.25 - 26.5625 = 2.6875 cm2 ( 2 ) - ( 3 ) = 32.0625 - 29.25 = 2.8125 cm2 ( 2 ) - ( 3 ) > ( 3 ) - ( 1 ) So, Accumulated error = ( 2 ) - ( 3 ) = 2.8125 cm2其他解答:
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