Bounds

Bounds

  • Bounds or boundaries are the upper and lower limit values that a number can be. They are used to indicate the degree of accuracy of a number.
  • A number is also referred to as being accurate to a certain level depending on the limits of its bounds. For instance, if the lower bound of a number is 4.5 and the upper bound is 5.5, the number can be said to be accurate to the nearest 1.

Upper and Lower Bounds

  • The upper bound of a given set of numbers is the largest number in that set.
  • The lower bound is the smallest number in the given set.
  • When given a problem involving bounds, always remember to consider both the lower and upper bound.

Error Intervals

  • The range between the lower and upper bound is known as the error interval and it’s used to quantify the uncertainty or level of accuracy in a measurement.
  • An error interval is commonly written in the format x≤n<x±d, where n is the rounded number and d is the rounding unit.

Working Out Bounds

  • To work out the lower bound of a rounded number, subtract half of the degree of accuracy from the number, and for the upper bound, add half of the degree of accuracy.
  • For example, if a number is 6 (to the nearest integer), then the lower bound of this value is 5.5 and the upper bound is 6.5.

Combining Bounds

  • When combining measurements (e.g. adding, subtracting, multiplying or dividing), remember that the measurement with the biggest percentage error will have the greatest effect on the accuracy of the result.

Dangers of Rounding Too Early

  • Avoid rounding too early in calculations. This can lead to final result inaccuracies. Always round your final answer.

Calculators and Bounds

  • Many calculators automatically round the results, so always consider bounds when using calculators in solving problems.