Rules For Upper And Lower Bounds

Upper and Lower bounds are a topic of mathematics, grouped under `number` and act as a measure of accuracy.

Assuming a measurement of a card to be 5cm, in terms of width, and measured to the nearest centimetre, the lower bound would be 4.5cm and the upper bound would be 5.5cm.

Students often lose marks on such exam questions due to the different rules that are used to complete calculations. Rules are as follows:

For an overall upper bound (UB):

Addition calculation UB + UB

Subtraction calculation UB - LB

Multiplication calculation UB x UB

Division calculation UB/LB

For an overall Lower Bound (LB):

Addition calculation LB + LB

Subtraction calculation LB - UB

Multiplication calculation LB x LB

Division calculation LB/UB

Note: Different values can be given to different degrees of accuracy in examination questions, so be sure to take care when working on upper and lower bound calculations.

Worked Example

A length of rope is measured at 150 cm long, correct to 2 significant figures. A piece of rope 50 cm long is cut off, measured correct to the nearest cm.

Calculate the upper bound, in cm, for the amount of rope left on original length.

LB for length of rope is 145cm

UB for length of rope is 155 cm

LB for length of rope cut off is 49.5 cm

UB for length of rope cut off is 50.5 cm

Therefore the upper bound, for amount of rope left is 155 cm - 49.5 cm = 105.5 cm