To calculate numbers with high precision beyond the typical 19 digits, multi-precision arithmetic is essential. This approach involves storing the digits of a number in separate arrays or classes and performing arithmetic operations on these individual digits. Various algorithms exist for addition, subtraction, multiplication, and division in multi-precision, which can be found through online searches. Another method suggested is using string inputs for numbers, allowing for calculations by aligning the digits and processing them in reverse order. For those using programming languages like C++, declaring a 64-bit variable can accommodate large integers, but it is limited to specific compilers. In Unix systems, alternatives like int64_t or uint64_t are recommended. Ultimately, utilizing a dedicated big number library is advised for handling calculations that exceed standard data type limits.