Upper and Lower Bounds

Upper and Lower Bounds


When combining upper and lower bounds, it is necessary to work out how the measurements relate to one another.

upper and lower bounds arithmetic


1. A shelf is being fitted into an alcove. The shelf is 2.3m long, with an error interval of 5cm; and the alcove is 2.4m long, with an error interval of 5cm. What is the biggest gap that there might be when fitting the shelf to the alcove?

Answer: 0.15m

The gap is given by the smallest shelf size and the largest alcove size.

Shelf lower bound: 2.3 - 0.05 ÷ 2 = 2.275

Alcove Upper Bound = 2.4 + 0.05 ÷ 2 = 2.425

Difference = 2.425 - 2.275 = 0.15m

2. Crates are being loaded onto a pallet for lifting by a crane. The maximum weight the crane can lift is 1000kg. Each crate weighs 85kg, to the nearest kg. What is the maximum number of crates to go on the pallet?

Answer: 11 crates

Higher bound for each crate = 85 + 0.5 = 85.5kg.

1000 ÷ 85.5 = 11.69.

Rounding 11.69 is not appropriate as this could take it over the safety limit.