UK EDITION
Help
Login
This worksheet is about finding upper and lower bounds.
Suppose we've rounded a number to the nearest whole number and get 14.
Numbers that round up to 14 include 13.9, 13.75, 13.694, 13.5. The smallest of these is 13.5. This is called the LOWER BOUND.
Anything smaller will round down to 13.
Larger numbers that round down to 14 include 14.1, 14.34968, 14.49. The largest of these is 14.4999999... This is the UPPER BOUND, which we write as 14.5.
Example 1
A room measures 433 cm by 372 cm, measured to the nearest centimeter.
Find the greatest and least possible areas of the room.
Answer
Upper bounds of measurements: 433.5 cm and 372.5 cm.
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 100 m in 12.8s.
The distance is measured to the nearest centimeter and the time to the nearest tenth of second.
Find the greatest and least possible speeds of the sprinter.
Answer
Upper bounds of measurements: 100.005 m and 12.85s
Lower bounds of measurements: 99.995 m 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}
8.89  8.81  8.74  8.47  
greatest speed  
least speed 
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}
8.89  8.86  8.78  8.47  
greatest speed  
least speed 
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}
8.04  8.74  8.65  7.96  
greatest speed  
least speed 
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
28.1  33  39.8  39.4  
greatest speed  
least speed 
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}
7.99  7.97  7.91  7.78  
greatest speed  
least speed 