PrecisionConstant

PrecisionConstant[ value, n ] represents a number rounded to n decimals, which also stands for all values that round to it.

Usages

`PrecisionConstant[ value, n ]`

PrecisionConstant[ value, n ] is displayed as value with exactly n decimals. It represents every number that rounds to that value, so it can be used for measured or rounded values. Calculations keep track of the precision, and when an answer is compared with a PrecisionConstant, any value within its precision matches. Approximate creates a PrecisionConstant from any numerical value.

Example	in	displayed
Two decimals: `3.1` is displayed as `3.10`.	`PrecisionConstant[ 3.1, 2 ]`	$3.10$
The value is rounded to `n` decimals for display.	`PrecisionConstant[ 3.14159, 2 ]`	$3.14$
Calculations keep the precision.	`CalcPlus[ PrecisionConstant[3.14, 2], 1 ]`	$4.14$

Example	in	out
`3.1415` rounds to `3.14`, so it matches.	`IsMatch[ PrecisionConstant[3.14, 2], 3.1415, Method=>accuracy ]`	`True`

Options

`LowerBound` and `UpperBound`

Set the range of values that the number represents explicitly, instead of deriving it from the rounding. The upper bound is not included.

Syntax	Example	out
`PrecisionConstant[ value, n, LowerBound=>a, UpperBound=>b ]`	`IsMatch[ PrecisionConstant[2.2, 1, LowerBound=>2.1, UpperBound=>2.3], 2.25, Method=>accuracy ]`	`True`
	`IsMatch[ PrecisionConstant[2.2, 1, LowerBound=>2.1, UpperBound=>2.3], 2.35, Method=>accuracy ]`	`False`

`Precision`

Give the number of significant digits instead of the number of decimals; the second argument is then left out.

Syntax	Example	displayed
`PrecisionConstant[ value, Precision=>p ]`	`PrecisionConstant[ 1234, Precision=>2 ]`	$12\times 10^{2}$

Details

Without n: PrecisionConstant[ 3.14 ] is just the number 3.14.
value must be a number: PrecisionConstant[ x, 2 ] is left unevaluated.

Invalid input	Result
`PrecisionConstant[ 3.14, 2, Foo=>1 ]`	Error: Invalid associative argument for PrecisionConstant: Foo

Warning

== does not consider a PrecisionConstant equal to an ordinary number: PrecisionConstant[3.14159, 2] == 3.14 is False. Use IsMatch with Method=>accuracy to check whether a value is within the precision.

See also: Approximate, Precision, IsMatch, Numerical

PrecisionConstant