Final answer:
To find the difference between the arithmetic and weighted average ROR, one must use a calculator or software to correctly compute each one. The difference is then obtained by subtraction, ensuring that rounding rules are followed and significant figures are considered to obtain an accurate result.
Step-by-step explanation:
To calculate the difference between the arithmetic average rate of return (ROR) and the weighted average rate of return (ROR), you would first have to compute the arithmetic average ROR by summing up all the individual rates of return and then dividing by the number of periods. The weighted average ROR is calculated by taking each rate of return, multiplying it by its respective weight (based on capital invested or time period), summing these products, and then dividing by the sum of the weights. To provide the precise answer, you would need specific values for the returns and their weights. However, you can use technology, such as a calculator or spreadsheet software, to quickly perform these computations and find the difference, rounding to the nearest tenth of a percent as required.
The importance of following proper rounding rules in calculations cannot be overstated. If mathematical operations are performed in a series of steps, one must keep track of significant figures and avoid rounding off intermediate answers, as this could lead to a less accurate final result. Always carry as many digits as possible from the intermediate answers to the next calculation step and round off the final answer according to the significant figures of the values used in the calculations.
For example, when analyzing the weight of a 5-lb bag of apples and determining its percent uncertainty, the equation used to find percent uncertainty is ∆A/A, where ∆A is the uncertainty in weight and A is the average weight. If A = 5.1 lb and ∆A = 0.3 lb, then the percent uncertainty is (0.3 lb / 5.1 lb) × 100, which equals approximately 5.9%. Notice the units cancel, rendering the result dimensionless.