# Limits of Accuracy What are they? Any measurement we make is rounded to some degree of accuracy or other  Nearest metre  Nearest litre The degree of.

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Limits of Accuracy

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

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

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

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

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)

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

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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