Evaluate numerically:

Value at two consecutive half-integers:

Complex number inputs:

Single-argument Round always returns an exact result:

The two-argument form tracks the precision of the second argument:

Evaluate efficiently at high precision:

Round can deal with real‐valued intervals:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix Round function using MatrixFunction:

Compute average-case statistical intervals using Around:

Values of Round at fixed points:

Value at 0:

Value at Infinity:

Evaluate symbolically:

Manipulate Round symbolically:

Find a value of x for which Round[x,2]=2:

Plot the Round function:

Visualize the two-argument form:

Plot Round in three dimensions:

Visualize Round in the complex plane:

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:

It has both singularities and discontinuities:

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:

First derivative with respect to x:

First derivative with respect to a:

Evaluate an integral:

Series expansion: