Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

N

N[expr]
gives the numerical value of expr.

N[expr,n]
attempts to give a result with ndigit precision.

DetailsDetails

• Unless numbers in expr are exact, or of sufficiently high precision, N[expr,n] may not be able to give results with ndigit precision.
• N[expr,n] may internally do computations to more than n digits of precision.
• \$MaxExtraPrecision specifies the maximum number of extra digits of precision that will ever be used internally.
• The precision n is given in decimal digits; it need not be an integer.
• n must lie between \$MinPrecision and \$MaxPrecision. \$MaxPrecision can be set to Infinity.
• n can be smaller than \$MachinePrecision.
• N[expr] gives a machineprecision number, so long as its magnitude is between \$MinMachineNumber and \$MaxMachineNumber.
• N[expr] is equivalent to N[expr,MachinePrecision].
• N[0] gives the number 0. with machine precision.
• N converts all nonzero numbers to Real or Complex form.
• N converts each successive argument of any function it encounters to numerical form, unless the head of the function has an attribute such as NHoldAll.
• You can define numerical values of functions using N[f[args]]:=value and N[f[args],n]:=value.
• N[expr,{p,a}] attempts to generate a result with precision at most p and accuracy at most a.
• N[expr,{Infinity,a}] attempts to generate a result with accuracy a.
• N[expr,{Infinity,1}] attempts to find a numerical approximation to the integer part of expr.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Evaluate numerically:

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Evaluate numerically to 50-digit precision:

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With machine-precision input, the results are always machine precision:

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With exact input, the results can be to the precision specified:

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