Which term describes errors caused by invalid operations such as dividing by zero?

The term that describes errors caused by invalid operations, such as dividing by zero, is a run-time error. Run-time errors occur during the execution of a program, often when the program encounters an operation that is mathematically or logically impossible—such as attempting to divide a number by zero, accessing a null reference, or exceeding an array's bounds.

When the program reaches this point during execution, it cannot complete the operation, resulting in the error. This type of error is distinct because it does not prevent the program from compiling (which is the case for syntax errors), but it does stop the program's normal operation when it runs into these invalid situations.

Understanding run-time errors is crucial for effective debugging and ensuring robust software development, as they indicate underlying issues in the logic or assumptions within the code that are only revealed during execution.