Bounds

• “Bounds” refer to the highest or lowest possible value a quantity can take. Specifically, the ‘upper bound’ is the highest possible value while the ‘lower bound’ is the lowest possible value.
• The concept of bounds is used in calculations where the numbers used are only known to a certain degree of accuracy.
• To apply the concept of bounds, consider a round-off number like 7.5 cm. Given it is rounded off to one decimal place, the upper and lower bounds could be 7.55 cm and 7.45 cm respectively. This is due to the usual method of rounding to a nearest value.
• The “error interval” is the range of values that a rounded number can take, i.e., the interval between the lower and upper bounds.
• When performing calculations with bounded numbers, the operation will also affect the way you calculate the possible bounds. For instance, when adding or subtracting numbers, consider the most extreme possibilities for each number— their highest and lowest bounds.
• However, when multiplying or dividing, remember that the bounds could multiply or divide to a value which is not within the original bounds. In these cases, reconsider the possible minimum and maximum values given the new calculation.
• It is worthy to understand that not all numbers have bounds – for instance, irrational or indefinite numbers, as their exact values cannot be determined.
• Bounds come into play considerably in real-life situations where measurements are taken and recorded to a certain degree of accuracy, such as physical or scientific experiments.
• Practice problems and exercises will be essential in understanding and applying the concept of bounds in numerical calculations.
• Key tips to remember: upper bound is the maximum, lower bound is the minimum, consider your operations (addition, subtraction, multiplication, division), and apply to real-world contexts!