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Apply Knowledge of Upper and Lower Bounds

In this worksheet, students will use upper and lower bounds in order to calculate areas and speeds from the given information.

'Apply Knowledge of Upper and Lower Bounds' worksheet

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Round/Approximate Numbers Appropriately

Difficulty level:  

Worksheet Overview

This activity is about calculating 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, etc.

The smallest of these is 13.5.

This is then called the lower bound.

Anything smaller than 13.5 will round down to 13.


Larger numbers that round down to 14 include 14.1, 14.34968, 14.49, etc. 

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 centimetre.

Find the greatest and smallest possible area of the room.



Upper bounds of measurements: 433.5 cm and 372.5 cm.

Greatest area is 433.5 × 372.5 = 161478.75 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 centimetre and the time to the nearest tenth of a 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 here!

For the greatest speed, we want the maximum distance in the minimum time:

  Greatest speed =
 = 7.84 ms-1 (3 s.f.)


For the least speed, we want the minimum distance in the maximum time:

  Least speed =
 = 7.78 ms-1 (3 s.f.)




Now it's over to you.

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