Calculating upper and lower bounds

Understanding Upper and Lower Bounds

The upper bound is the highest possible value a measurement can be. When a value is rounded up, we talk about its upper bound.
The lower bound is the lowest possible value a measurement can be. When a value is rounded down, it has a lower bound.
The idea of bounds comes into effect because measurements can never be made to perfect accuracy. Therefore, there is a limit of precision set by the equipment used or the method of measurement.
The two bounds provides the interval within which the accurate value can lie.

To calculate the upper and lower bounds of a rounded number, you must first identify the degree of accuracy.
The degree of accuracy can be a whole number, decimal or given to a number of significant figures.
The lower bound is calculated by subtracting half of the degree of accuracy from the rounded number.
The upper bound is calculated by adding half of the degree of accuracy to the rounded number.

The concept of upper and lower bounds is critical in handling measurements in practical applications. For instance, in building and construction, bounds are used to account for tolerances in material measurements.
It is important to note that whilst dealing with upper and lower bounds, all calculations performed must maintain the same level of precision for accuracy.

Misunderstanding the concept of degree of accuracy and how it impacts the calculation of upper and lower bounds.
Failing to maintain consistency in the degree of accuracy through all calculations.
Neglecting the application of bounds when dealing with measurements in real world problems.
Mistaking the rounded value for an exact value, forgetting that it is just an approximation within a known interval.