- Mathematical function, suitable for both symbolic and numerical manipulation.
- Round rounds numbers of the form x .5 toward the nearest even integer.
- Round[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.
- Round[x] applies separately to real and imaginary parts of complex numbers.
- If a is not a real number, Round[x,a] is given by the formula Round[x,a]a Round[x/a]. »
- For exact numeric quantities, Round internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- Round automatically threads over lists.
Examplesopen allclose all
Basic Examples (3)
Numerical Evaluation (7)
Single-argument Round always returns an exact result:
Round threads elementwise over lists:
Round can deal with real‐valued intervals:
Specific Values (6)
Function Properties (10)
Round[x] is defined for all real and complex inputs:
Round[x,a] is defined for a!=0:
Round can produce infinitely large and small results:
Round is an odd function in its first argument:
Round is an even function in its second argument:
Round is not an analytic function:
Round is nondecreasing:
Round is not injective:
Round is not surjective:
Round is neither non-negative nor non-positive:
Round is neither convex nor concave:
Properties & Relations (6)
Round[x,a] gives the multiple of a nearest to x:
At midpoints, Round rounds toward even integers:
Possible Issues (1)
Round does not automatically resolve the value:
Wolfram Research (1988), Round, Wolfram Language function, https://reference.wolfram.com/language/ref/Round.html (updated 2007).
Wolfram Language. 1988. "Round." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/Round.html.
Wolfram Language. (1988). Round. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Round.html