Upper and Lower Bounds
• Introduction

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.

Upper bounds of measurements: 433.5cm and 372.5cm.

Greatest area is 433.5×372.5 = 161,478.75 cm2.

Lower bounds of measurements: 432.5 cm and 371.5 cm.

Least area is 432.5×371.5 = 160,673.75 cm2.

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.

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 =
 100.005 12.75
= 7.84 ms-1 (3 s.f.)

For the least speed we want the min. distance in the max. time.

Least speed =
 99.995 12.85
= 7.78 ms-1 (3 s.f.)
• Question 1

Find the greatest and least areas of a room with the following measurements:

358 cm by 332 cm

Greatest area is ___________ cm2 .

Least area is ___________ cm2.

 greatestarea leastarea 119 201.25 134 321.25 118 511.25 133 573.25
• Question 2

Find the greatest and least areas of a room with the following measurements:

297 cm by 451 cm

Greatest area is ___________ cm2 .

Least area is ___________ cm2.

 greatestarea leastarea 119 201.25 134 321.25 118 511.25 133 573.25
• Question 3

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.

 greatestspeed leastspeed 8.89 8.81 8.74 8.47
• Question 4

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.

 greatestspeed leastspeed 8.89 8.86 8.78 8.47
• Question 5

Find the greatest and least areas of a room with the following measurements:

447 cm by 314 cm

Greatest area is ___________ cm2 .

Least area is ___________ cm2.

 greatestarea leastarea 119 201.25 140 738.75 118 511.25 139 977.75
• Question 6

Find the greatest and least areas of a room with the following measurements:

3 m by 4m

Greatest area is ___________ m2 .

Least area is ___________ m2.

 greatestarea leastarea 15.75 11.25 12.25 8.75
• Question 7

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.

 greatestspeed leastspeed 8.04 8.74 8.65 7.96
• Question 8

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

 greatestspeed leastspeed 28.1 33 39.8 39.4
• Question 9

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.

 greatestspeed leastspeed 7.99 7.97 7.91 7.78
• Question 10