Approximate

Approximate[ expr, n ] rounds a numerical value to n decimals, and keeps track of the rounding.

Usages

`Approximate[ expr, n ]`

Approximate[ expr, n ] calculates the value of expr and rounds it to n decimals. The result is a PrecisionConstant: a number that remembers its precision. Later calculations use the exact value, and when an answer is checked, any value that rounds to the same number matches. Use Numerical instead if you only need a decimal number.

Example	in	displayed
`π` to `2` decimals.	`Approximate[ Pi, 2 ]`	$3.14$
A fraction.	`Approximate[ 1/3, 2 ]`	$0.33$
An expression with a numerical value.	`Approximate[ 2*Pi + 1, 2 ]`	$7.28$
Halves are rounded up.	`Approximate[ 2.45, 1 ]`	$2.5$
Each element of a list.	`Approximate[ {Pi, EulerE}, 2 ]`	$\{3.14, 2.72\}$

`Approximate[ expr ]`

Without n, the value is calculated as a decimal number, as with Numerical.

Example	in	out
The value of `π`.	`Approximate[ Pi ]`	`3.14159265359`

Options

`RoundingMode`

How to round: 'Default' (halves up), 'Floor' (always down) or 'Ceil' (always up).

Syntax	Example	displayed
`Approximate[ expr, n, RoundingMode=>'Floor' ]`	`Approximate[ 2.45, 1, RoundingMode=>'Floor' ]`	$2.4$
`Approximate[ expr, n, RoundingMode=>'Ceil' ]`	`Approximate[ 2.41, 1, RoundingMode=>'Ceil' ]`	$2.5$

`OmitTrailingZeroes`

If set to False, the result is displayed with exactly n decimals. Default: True.

Syntax	Example	displayed
`Approximate[ expr, n, OmitTrailingZeroes=>False ]`	`Approximate[ 2.5, 3, OmitTrailingZeroes=>False ]`	$2.500$

`RoundInteger`

If set to True, integers are also given a precision. Default: False, so integers are not changed: Approximate[ 2, 1 ] gives 2.

Syntax	Example	displayed
`Approximate[ expr, n, RoundInteger=>True ]`	`Approximate[ 2, 1, RoundInteger=>True ]`	$2.0$

Details

Variables: an expression with variables is not changed: Approximate[ x + Pi, 2 ] gives x+Pi. Use Numerical[ x + Pi, 2 ] to round the numbers in it.

Invalid input	Result
`Approximate[ 2.45, 1, RoundingMode=>'Up' ]`	Error: Invalid value for RoundingMode: 'Up'