Final answer:
The error, relative error, and number of significant digits can be calculated for given approximations.
Step-by-step explanation:
Error: The error is the absolute difference between the approximation xa and the true value xt.
Relative Error: The relative error is the ratio of the absolute error to the true value xt, expressed as a percentage.
Number of Significant Digits: The number of significant digits in an approximation is equal to the number of digits that can be considered reliable and accurate. To determine the number of significant digits in a number, count the number of digits from the first non-zero digit to the last non-zero digit.
Using the given information, we can determine the error, relative error, and number of significant digits in the given approximations.
a. 22.4 x 8.314 = 186.4336
Error: |186.4336 - 187.8848| = 1.4512
Relative Error: (1.4512 / 187.8848) x 100% = 0.7713%
Number of Significant Digits: 3
b. 1.381 x 6.02 = 8.32962
Error: |8.32962 - 8.28| = 0.04962
Relative Error: (0.04962 / 8.28) x 100% = 0.5984%
Number of Significant Digits: 6