Precision

How many significant decimal digits a number carries.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguagePrecision!↗

Precision(expr)$PositiveInfinity$ for an exact number, MachinePrecision for a machine number, otherwise its significant decimal digit count.

Typed signatures

Type	Package	Applies
(any) -> integer<1..> | real | signed_infinity	combinatorics	always

Domain: Collections

Details

• Exact numbers (integers, rationals, radicals, symbolic constants like $\pi$) carry infinite precision, Wolfram's own convention.
• A literal of up to 17 digits (what a double holds) is a machine number: its precision is the symbol MachinePrecision, as in Wolfram.
• A literal with more digits counts the digits actually written; Wolfram's count is not an integer (20.497 for 21 digits).

Examples

2 more kept as data, checked against the oracles

Basic #

live ↗

In$\mathrm{Precision}(2)$Out$∞$

Exact numbers carry infinite precision

live ↗

In$\mathrm{Precision}(\frac{6}{5})$Out$∞$

Scope #

An exact rational also carries infinite precision

live ↗

In$\mathrm{Precision}(\frac{1}{3})$Out$∞$

A machine number's precision is the symbol MachinePrecision

live ↗

In$\mathrm{Precision}(2.5)$Out$\mathrm{MachinePrecision}$

A double's sixteen digits are still a machine number

live ↗

In$\mathrm{Precision}(3.141\,592\,653\,589\,793)$Out$\mathrm{MachinePrecision}$

Symbolic expressions with exact coefficients also report infinite precision

live ↗

In$\mathrm{Precision}(5x^2+3)$Out$∞$

About

Examples	8
Checked against	Wolfram Language 7 agree1 differ
Crosswalk	Wolfram Language

See also: IsMachineNumber, IsNumeric