# Bounds

• Bounds
• Upper and lower bounds
• When a measurement is rounded to a given unit, the actual measurement can be anything up to half a unit bigger or smaller
• When a measurement is truncated to a given unit, the actual measurement can be a whole unit smaller or bigger
• Maximum and minimum values for calculations
• When a calculation is done using rounded values there will be a discrepancy between the calculated value and the actual value
• The lower bound (lowest number the rounded number could be) will be bigger then or equal to
• The upper bound (highest number the rounded number could be) will be less than
• In a calculation where more then one value has been rounded you need to think what bounds to use to get the highest or lowest values that the calculation could equal
• Subtracting: Lowest value would be to have the LB of the first number and the UB of the second number
• Division: To get the lowest value use the lower bound of the first number and the UB of the second number
• Addition: To get the lowest value use both LB, to get highest value use both UB
• Multiplication: To get the lowest value use both LB, to get the highest value use both UB