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 77 75.5 ≤ Height < 76.5 76.49999999999999999….. 76.5 Limits of Accuracy 76 75.5 75

Example 2 A car is 2.6m long, measured correct to 1 decimal place The range of values between the Upper & Lower Bounds is often referred to as the rounding error 2.55 ≤ Length < 2.65 2.50 2.6 2.60 2.70 2.55 2.65 Lower Bound Upper Bound

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

6.35m 6.4m 6.45m 4.35m 4.3m 4.25m MINIMUM AREA 6.35 x 4.25 = 26.9875m2 = 26.99m2 (2 dp)

Limits of Accuracy 6.35m 6.4m 6.45m 26.99 ≤ Area < 28.06 m2 4.35m 4.3m 4.25m MAXIMUM AREA 6.45 x 4.35 = 28.0575 m2 = 28.06 m2 (2 dp)

Val is in training for a 400 metre race 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. 395 m 400 m 400 m 405 m 43.5 s 44 s 44.5 s Max speed = Greatest distance Shortest Time speed = 405 43.5 speed = distance time speed = 9.3103… m/s Max speed is the Greatest distance in the Shortest Time speed = 9.3 m/s (1 dp)