N

• 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 0. with machine precision.

• N converts all non-zero 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.

• See Section 1.1.2, Section 1.1.4, Section 3.1.4 and Section 3.1.5.

• Implementation notes: see Section A.9.4.

• See also: Chop, CompiledFunction, Rationalize, MachinePrecision, NHoldAll, RealDigits.

• New in Version 1; modified in 5.