# Arbitrary-Precision Calculations

When you use //N to get a numerical result, *Mathematica* does what a standard calculator would do: it gives you a result to a fixed number of significant figures. You can also tell *Mathematica* exactly how many significant figures to keep in a particular calculation. This allows you to get numerical results in *Mathematica* to any degree of precision.

expr//N or N[expr] | approximate numerical value of expr |

N[expr,n] | numerical value of expr calculated with n-digit precision |

Numerical evaluation functions.

This gives the numerical value of

to a fixed number of significant digits. Typing

N[Pi] is exactly equivalent to

Pi//N.

Out[1]= | |

This gives

to 40 digits.

Out[2]= | |

Here is

to 30 digits.

Out[3]= | |

Doing any kind of numerical calculation can introduce small roundoff errors into your results. When you increase the numerical precision, these errors typically become correspondingly smaller. Making sure that you get the same answer when you increase numerical precision is often a good way to check your results.

The quantity

turns out to be very close to an integer. To check that the result is not, in fact, an integer, you have to use sufficient numerical precision.

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