General Mathematic HSC Errors in Measurement Stage 6

General Mathematic (HSC) Errors in Measurement Stage 6 - Year 12 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use 1

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. 5 cm 4 – 0. 5 = 3. 5 cm End of Slide 2

Error in in Measurement Error Between what two limits does 75 m lie if measured with a trundle wheel to the nearest metre? Error = ± 0. 5 m Lower = 75 - 0. 5 = 74. 5 m Upper = 75 + 0. 5 = 75. 5 m End of Slide 3

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

Error in Measurement Between what two limits does 500 km lie if measured with a odometre to the nearest 5 km? Error = ± 2. 5 km Lower = 500 - 2. 5 = 497. 5 km Upper = 500 + 2. 5 = 502. 5 km Odometer End of Slide 5

Error in Measurement A building’s height was measured as 93 metres to the nearest metre. Between what limits does it lie? Range = 93 ± 0. 5 metres Between 92. 5 m and 93. 5 m. End of Slide 6

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

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

Error in Measurement These errors compound when dealing with area. 5 m 6 m Area = 5 x 6 = 30 m 2 Smallest Dimensions L = 5. 5 m B = 4. 5 m Smallest Area = 5. 5 x 4. 5 = 24. 75 m 2 Largest Dimensions L = 6. 5 m B = 5. 5 m Largest Area = 6. 5 x 5. 5 = 35. 75 m 2 Maximum Error = 35. 75 - 30 = 5. 75 m 2 End of Slide 9

Error in Measurement Percentage Error 5 m 6 m Area = 5 x 6 = 30 m 2 Maximum Error = 5. 75 m 2 Percentage Error = Maximum Error x 100% Area = 5. 75 x 100% 30 ≈ 19. 17% End of Slide 10

Error in Measurement These errors are more compounded when dealing with volume. 5 m Volume = 6 x 4 x 5 = 120 m 3 Smallest Dimensions 6 m L = 5. 5 m B = 3. 5 m H = 4. 5 m Smallest Volume = 5. 5 x 3. 5 x 4. 5 = 86. 625 m 3 4 m Largest Dimensions L = 6. 5 m B = 4. 5 m H = 5. 5 m Largest Volume = 6. 5 x 4. 5 x 5. 5 = 160. 875 m 3 Maximum Error = 160. 875 - 120 = 40. 875 m 3 End of Slide 11

Error in Measurement These errors are more compounded when dealing with volume. 5 m 6 m 4 m Volume = 6 x 4 x 5 = 120 m 3 Maximum Error = 40. 875 m 3 Percentage Error = Maximum Error x 100% Volume = 40. 875 x 100% 120 ≈ 34. 0625% End of Show 12