Numerical

Numerical[ expr ] returns the approximate numerical value of an expression, optionally rounded to a number of decimals.

Usages

`Numerical[ expr ]`

Numerical[ expr ] calculates the decimal value of expr. Integers stay integers. If expr contains variables, only the numerical parts are calculated.

Example	in	out
The value of `Pi`.	`Numerical[ Pi ]`	`3.14159265359`
An integer result.	`Numerical[ 3^2 + 9 ]`	`18`
A fraction with a finite decimal representation.	`Numerical[ 1/4 ]`	`0.25`
A script variable.	`x := Sin[1] r := Numerical[x]`	`r = 0.841470984808`
Only the numerical part is calculated.	`Numerical[ x + Pi ]`	`x+3.14159265359`

`Numerical[ expr, n ]`

Numerical[ expr, n ] rounds the value to n decimals. A negative n rounds to tens, hundreds, and so on. Halves are rounded up.

Example	in	out
Round to `3` decimals.	`x := Sin[1] r := Numerical[x, 3]`	`r = 0.841`
Round to `2` decimals.	`Numerical[ Pi, 2 ]`	`3.14`
`0.25` rounded to `1` decimal.	`Numerical[ 1/4, 1 ]`	`0.3`
Round to hundreds.	`Numerical[ 1234.5678, -2 ]`	`1200`
Round each element of a list.	`Numerical[ {Pi, Sqrt[2]}, 2 ]`	`{3.14, 1.41}`

Details

Integers are not changed: Numerical[ 2, 2 ] gives 2, not 2.00.
Trailing zeros are not displayed: Numerical[ 1/4, 3 ] is displayed as $0.25$ .
Repeating decimals: without n, a value such as 1/3 is calculated with 16 digits. Give a number of decimals to get a short result.
Numerical[ NaN ] gives NaN.

See also: Round, Floor, Ceil, DecimalToFraction