BUILT-IN MATHEMATICA SYMBOL

# N

N[expr]
gives the numerical value of expr.

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

## DetailsDetails

• Unless numbers in expr are exact, or of sufficiently high precision, N[expr, n] may not be able to give results with n-digit 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 machine-precision number, so long as its magnitude is between \$MinMachineNumber and \$MaxMachineNumber.
• N[expr] is equivalent to N[expr, MachinePrecision].
• N[0] gives the number 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:

 Out[1]=

Evaluate numerically to 50-digit precision:

 Out[1]=

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

 Out[1]=

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

 Out[2]=