numerics - Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays

0.333333

as the result. When I copy that output to use elsewhere, the paste produces

0.3333333333333333`

What is the meaning and function of the backtick ?

I realize this must be quite elementary. I stand ready to be educated. :-)

Answer

The backtick is a short-hand to mark the precision of your output. If it is not followed by any number, it denotes machine precision. You can denote arbitrary precision by including a number, as for example, 0.3`20.

By default, these are not displayed in StandardForm, which is why you see them only when copying, at which point it gets converted to InputForm. You can show them with NumberMarks -> True. For example:

Sqrt[2] // N
(* 1.4142135623730951 *)

InputForm[Sqrt[2] // N, NumberMarks -> True]
(* 1.4142135623730951` *)

Comments

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