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N

N[expr]
gives the numerical value of expr.
N[expr, n]
attempts to give a result with n-digit precision.
  • 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[0] gives the number 0. with machine precision.
  • 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.
EXAMPLESCLOSE ALL
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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Click for copyable input
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With exact input, the results can be to the precision specified:
In[2]:=
Click for copyable input
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