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This worksheet is about finding upper and lower bounds.
Example 1
A room measures 433cm by 372cm, measured to the nearest cm.
Find the greatest and least possible areas of the room.
Answer
Upper bounds of measurements: 433.5cm and 372.5cm.
Greatest area is 433.5×372.5 = 161,478.75 cm^{2}.
Lower bounds of measurements: 432.5 cm and 371.5 cm.
Least area is 432.5×371.5 = 160,673.75 cm^{2}.
Example 2
A sprinter runs 100m in 12.8s.
The distance is measured to the nearest cm and the time to the nearest tenth of second.
Find the greatest and least possible speeds of the sprinter.
Answer
Upper bounds of measurements: 100.005m and 12.85s
Lower bounds of measurements: 99.995m and 12.75s.
Be careful! For the greatest speed we want the max. distance in the min. time.
Greatest speed = 

= 7.84 ms^{1} (3 s.f.) 
For the least speed we want the min. distance in the max. time.
Least speed = 

= 7.78 ms^{1} (3 s.f.) 
Find the greatest and least speeds from the following information:
100.03 m (to the nearest cm) covered in 11.4 s (to the nearest tenth second)
Greatest speed is ___________ ms^{1} .
Least speed is ___________ ms^{1}.
greatest speed  least speed  
8.89  
8.81  
8.74  
8.47 
Find the greatest and least speeds from the following information:
99.70 m (to the nearest cm) covered in 11.3 s (to the nearest tenth second)
Greatest speed is ___________ ms^{1} .
Least speed is ___________ ms^{1}.
greatest speed  least speed  
8.89  
8.86  
8.78  
8.47 
Find the greatest and least speeds from the following information:
100 m (to the nearest m) covered in 12 s (to the nearest second)
Greatest speed is ___________ ms^{1} .
Least speed is ___________ ms^{1}.
greatest speed  least speed  
8.04  
8.74  
8.65  
7.96 
Find the greatest and least speeds from the following information:
99 miles (to the nearest mile) covered in 3 hours (to the nearest hour)
Greatest speed is ___________ mph
Least speed is ___________ mph
greatest speed  least speed  
28.1  
33  
39.8  
39.4 
Find the greatest and least speeds from the following information:
100.01 m (to the nearest cm) covered in 12.6 s (to the nearest tenth second)
Greatest speed is ___________ ms^{1} .
Least speed is ___________ ms^{1}.
greatest speed  least speed  
7.99  
7.97  
7.91  
7.78 