Final answer:
Adding two double numbers that exceeds the maximum representable value results in an arithmetic overflow, denoted as infinity. This follows the IEEE 754 standard for floating-point arithmetic. The concept of significant figures is also important in scientific calculations involving addition, subtraction, multiplication, and division.
Step-by-step explanation:
When you add two double numbers (a data type used in programming to represent floating-point numbers) and the result exceeds the maximum value that a double number can represent, the result is what's called an arithmetic overflow, which typically leads to a state called infinity. In most programming environments and mathematical calculations using a digital system, this state is denoted by the term 'Inf' or a special infinity symbol.
Modern computers follow the IEEE Standard for Floating-Point Arithmetic (IEEE 754), and when an overflow occurs in a double precision floating-point operation, the result is a positive infinity if both numbers are positive, or negative infinity if both numbers are negative. This is akin to saying that the result is larger than any finite double value that can be represented.
However, when performing scientific calculations, it's important to note the rules of significant figures. For instance, when performing addition and subtraction, the result should have the same number of decimal places as the least precise number. In multiplication and division, the answer should have the same number of significant figures as the number with the least significant figures.