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
76
75.5
75
Limits of
Accuracy
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
2.55
2.6
2.60
2.65
2.70
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
4.35m
4.3m
4.25m
MAXIMUM AREA
6.45 x 4.35
= 28.0575 m2
= 28.06 m2 (2 dp)
26.99 ≤ Area < 28.06 m2
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
405 m
43.5 s
44 s
44.5 s
Max speed = Greatest distance
Shortest Time
speed = 405
speed = distance
43.5
time
speed = 9.3103… m/s
Max speed is
speed = 9.3 m/s (1 dp)
the Greatest distance
in the Shortest Time