Upper & Lower Bounds (DP IB Applications & Interpretation (AI)): Revision Note

Upper & Lower Bounds

What are bounds?

• Bounds are the smallest (lower bound, LB) and largest (upper bound, UB) numbers that a rounded number can lie between

  • It simply means how low or high the number could have been before it was rounded

• The bounds for a number, , can be written as 

  • Note that the lower bound is included in the range of values could have taken but the upper bound is not

How do we find bounds?

• The basic rule is “half up, half down”

  • To find the upper bound add on half the degree of accuracy

  • To find the lower bound take off half the degree of accuracy

• Remember that the upper bound is the cut off point for the greatest value that the number could have been rounded from but will not actually round to the number itself

How do we calculate using bounds?

• Find bounds before carrying out the calculation and then use the rules:

  • To add UB = UB + UB and LB = LB + LB

  • To multiply UB = UB × UB and LB = LB × LB

  • To divide UB = UB / LB and LB = LB / UB

  • To subtract UB = UB - LB and LB = LB – UB

• Use logic to decide which bound to use within the calculation

  • For example if you are finding the maximum volume of a sphere with the radius given correct to 1 decimal place substitute the upper bound of the radius into your calculation for the volume