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  "body": "\n## Summary\n\nArbitrary-precision arithmetic computes with numbers whose number of digits is limited only by the memory of the computer, not by a fixed hardware format.\nIntegers and rational numbers can then be handled exactly, and real numbers with as many correct digits as one asks for.\nUnlike fixed-size [[floating-point arithmetic|RTKRSC3KPH]], each operation costs more as the numbers grow, so fast multiplication algorithms matter.\nIt is used in computer algebra, number theory, cryptography and to check numerical results with higher precision.\n\n## Explanations\n\n### L1 human\n\nA calculator shows perhaps $12$ digits, and a computer's built-in numbers hold about $16$ decimal digits.\nArbitrary-precision arithmetic stores a number as a list of digits that can be as long as needed, just as one writes long numbers on paper.\nIt can compute $2^{1000}$, a number with $302$ digits, exactly, or $\\pi$ to a million decimals.\nThe price is speed: a product of two numbers with $n$ digits each takes far more time than one machine multiplication.\n",
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