Upper and Lower Bounds (2)
• Introduction

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.

Upper bounds of measurements: 433.5 cm and 372.5 cm.

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 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.

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 =
 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

 119 201.25 134 321.25 118 511.25 133 573.25 greatestarea leastarea
• 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

 119 201.25 134 321.25 118 511.25 133 573.25 greatestarea leastarea
• 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

 8.89 8.81 8.74 8.47 greatestspeed leastspeed
• 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

 8.89 8.86 8.78 8.47 greatestspeed leastspeed
• 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

 119 201.25 140 738.75 118 511.25 139 977.75 greatestarea leastarea
• 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

 15.75 11.25 12.25 8.75 greatestarea leastarea
• 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

 8.04 8.74 8.65 7.96 greatestspeed leastspeed
• 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

 28.1 33 39.8 39.4 greatestspeed leastspeed
• 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

 7.99 7.97 7.91 7.78 greatestspeed leastspeed
• Question 10

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

268 cm by 320 cm

Greatest area is ___________ cm2

Least area is ___________ cm2

 86 054.25 140 738.75 85 466.25 139 977.75 greatestarea leastarea
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