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1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Errors in Measurement Stage 6 - Year 12 General Mathematic (HSC)

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2 Error in Measurement All measurements are accurate to within ± 0.5 of the smallest unit on the measuring device. = 4 cm Error = ±0.5 cm Actual Length lies between 4 + 0.5 =4.5cm 4 – 0.5 =3.5cm End of Slide

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3 Between what two limits does 75m lie if measured with a trundle wheel to the nearest metre? Lower = 75 -0.5 = 74.5 m Upper = 75 +0.5 = 75.5 m Error = ±0.5 m Error in Measurement End of Slide

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4 Between what two limits does 360cm lie if measured with a decimetre tape to the nearest 10cm? Lower = 360 - 5 = 355 cm Upper = 360 +5 = 365 cm Decimetre tape Error = ± 5 cm Error in Measurement End of Slide

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5 Between what two limits does 500 km lie if measured with a odometre to the nearest 5km? Lower = 500 - 2.5 = 497.5 km Upper = 500 +2.5 = 502.5 km Odometer Error = ± 2.5 km Error in Measurement End of Slide

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6 A building’s height was measured as 93 metres to the nearest metre. limits Between what limits does it lie? Range Range = 93 ± 0.5 metres Between 92.5m and 93.5 m. Error in Measurement End of Slide

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7 80cm 10cm A ball was measured as 80cm to the nearest 10cm. limits Between what limits does it lie? Range Range = 80 ± 5cm Between 75cm and 85 cm. Error in Measurement End of Slide

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8 Port Macquarie Sydney 500km 100km The distance from Port Macquarie to Sydney is given as 500km to the nearest 100km. limits Between what limits does it lie? Range Range = 500 ± 50km Between 550km and 650km. Error in Measurement End of Slide

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9 These errors compound when dealing with area. 6m 5m Smallest Dimensions L = 5.5m B = 4.5m Area = 5 x 6 = 30m 2 Smallest Area = 5.5 x 4.5= 24.75 m 2 Largest Dimensions L = 6.5m B = 5.5m Largest Area = 6.5 x 5.5= 35.75 m 2 Maximum Error = 35.75- 30 = 5.75 m 2 Error in Measurement End of Slide

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10 Percentage Error 6m 5m Area = 5 x 6 = 30m 2 Maximum Error = Maximum Error = 5.75 m 2 Percentage Error = Maximum Error Area x 100% 5.75 30 x 100% = ≈ 19.17% Error in Measurement End of Slide

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11 These errors are more compounded when dealing with volume. 6m 5m Smallest Dimensions L = 5.5m B = 3.5m Volume = 6 x 4 x 5 = 120m 3 Smallest Volume = 5.5 x 3.5 x 4.5 = 86.625 m 3 Largest Dimensions L = 6.5m B = 4.5m Largest Volume = 6.5 x 4.5 x 5.5= 160.875 m 3 Maximum Error = 160.875- 120 = 40.875 m 3 4m H = 4.5m H = 5.5m Error in Measurement End of Slide

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12 These errors are more compounded when dealing with volume. 6m 5m Volume = 6 x 4 x 5 = 120m 3 Maximum Error = Maximum Error = 40.875 m 3 4m Percentage Error = Maximum Error Volume x 100% 40.875 120 x 100% = ≈ 34.0625% Error in Measurement End of Show

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