Limits of Accuracy

1
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

3
For example

• A lighthouse is 76m tall, measured to the
  nearest metre

77
75.5 Height lt 76.5
76.49999999999999999..
76.5
Limits of Accuracy
76
75.5
75
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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 lt 2.65
2.6
2.60
2.70
2.50
2.55
2.65
Lower Bound
Upper Bound
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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
6
6.4m
6.45m
6.35m
4.35m
4.3m
4.25m
MINIMUM AREA
6.35 x 4.25
26.9875m2
26.99m2 (2 dp)
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Limits of Accuracy
6.4m
6.45m
6.35m
26.99 Area lt 28.06 m2
4.35m
4.3m
4.25m
MAXIMUM AREA
6.45 x 4.35
28.0575 m2
28.06 m2 (2 dp)
8
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 m
395 m
400 m
44 s
44.5 s
43.5 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)