Final answer:
Loss of significance errors can be avoided by rearranging the function, using a different evaluation method, increasing precision during calculations, and rounding off only at the final step, maintaining 'guard digits'.
Step-by-step explanation:
Loss of significance errors can be avoided by several means. First, rearranging the function being evaluated can help prevent subtraction of nearly equal numbers, which is a common cause of these errors. Second, using a different method of evaluation may be beneficial, especially if the first method is prone to numerical errors due to the nature of the operation. Third, increasing the precision of calculations by using more decimal places during intermediate steps can help mitigate rounding errors. It is recommended to keep additional significant figures during the process and round off only at the final result. This practice is often referred to as using a 'guard digit'.
Rounding the final result to the appropriate number of significant figures is necessary to correctly represent the certainty of the values used in the calculation. When performing operations such as multiplication or division, it is important to apply the rules of significant figures and maintain the units accordingly.
As a practical example, when calculating 5,098 - (5.000) × (1,010), keeping all significant figures during the calculation yields 48. However, rounding intermediate results to two significant figures changes the calculation to 5,100 - (5.000) × (1,000) = 100, leading to a significant error.