Final answer:
The question involves designing an application with robust defensive programming that can perform mathematical operations and record the results, while accounting for user input validation and the accuracy of significant figures.
Step-by-step explanation:
When designing an application that performs calculations, one must incorporate defensive programming practices. These practices ensure that the application can handle unexpected user inputs and events. For instance, when a user inputs two numbers and chooses an operation (+, -, *, or /), the application should first validate that the inputs are indeed numbers and that the operation is one of the allowed types. Upon successful calculation, the equation and its result should be recorded in equations.txt within the correct format, such as '21 + 3 = 24'.
Additionally, considering the rules of significant figures is essential. When adding two positive numbers, the answer will retain a positive sign. Conversely, adding two negative numbers keeps a negative sign. However, when adding numbers with opposite signs, subtract the smaller from the larger and assign the sign of the larger number. Subtraction involves inverting the subtracted number's sign before applying the addition rules.
It is crucial to remember that the calculator or computer's role is to execute calculations as instructed. Still, the precision of the calculation is dependent on the user's input. A calculator will often give a more precise number than the data warrants, and the user must determine the appropriate number of decimal places to report. Therefore, while the application can assist, it is ultimately the user's responsibility to assure the accuracy and significance of the presented data.