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Limits of Accuracy

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What are they? Any measurement we make is rounded to some degree of accuracy or other Nearest metre Nearest litre The degree of rounding gives the possible values of the measurement before rounding

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For example A lighthouse is 76m tall, measured to the nearest metre 76 75 77 76.49999999999999999….. 75.5 76.5 Limits of Accuracy 75.5 ≤ Height < 76.5

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Example 2 A car is 2.6m long, measured correct to 1 decimal place 2.62.602.702.50 2.552.65 Lower Bound Upper Bound The range of values between the Upper & Lower Bounds is often referred to as the rounding error 2.55 ≤ Length < 2.65

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Problems involving accuracy When we calculate an area or a volume, the errors in the measurements will give an even larger error For example, a room is measured as 6.4 x 4.3 metres, measured to 1 decimal place. Calculate the Limits of Accuracy of the area of the room

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6.4m 4.3m 6.45m6.35m 4.35m 4.25m MINIMUM AREA 6.35 x 4.25 = 26.9875m 2 = 26.99m 2 (2 dp)

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6.4m 4.3m 6.45m6.35m 4.35m 4.25m MAXIMUM AREA 6.45 x 4.35 = 28.0575 m 2 = 28.06 m 2 (2 dp) Limits of Accuracy 26.99 ≤ Area < 28.06 m 2

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Val is in training for a 400 metre race. He states that he can run 400 metres in 44 seconds. Both of these measurements are given to two significant figures. Find his maximum speed. 400 m 405 m395 m400 m 44 s44.5 s43.5 s speed = distance time speed = 405 43.5 speed = 9.3103… m/s speed = 9.3 m/s (1 dp) Max speed = Greatest distance Shortest Time Max speed is the Greatest distance in the Shortest Time

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