Dynamic Interpretation Button Label Loses Formatting on Copy and Paste

Question

I have an Interpretation Button that displays its label correctly on evaluation. However, when I copy and paste it as input the label loses its formatting.

Interpretation[{x = RandomReal[]}, Button[Dynamic[N[x, 6]], x = RandomReal[]], N[x, 6]]

When this is copy and pasted into an input cell it changes to:

How can I get it to retain its label formatting which should be the 6 decimal place number?

Also, I though N was cutting the number down to 6 significant figures. This is obviously not the case since the machine precision number is showing up in the label. What have I missed here, as well?

Answer 1

It happens because "Input" cell style has NumberMarks -> True while "Output" inherits default False.

You can set BaseStyle -> NumberMarks -> False for the Button:

Interpretation[
 {x = RandomReal[]}, 
 Button[Dynamic[N[x, 6]], x = RandomReal[], BaseStyle -> NumberMarks -> False], 
 N[x, 6]
]

Answer 2

As an option

Interpretation[{x = RandomReal[]}, Button[Dynamic@ToString@SetPrecision[x, 6], 
               x = RandomReal[]], N[x, 6]]

Or

Interpretation[{x = RandomReal[]}, Button[Dynamic@N@Round[x, 1*^-6], 
               x = RandomReal[]], N@Round[x, 1*^-6]]

As far as I understand, N really doesn't change anything about a machine number, not even its precision, it does most of the work on exact inputs. So for machine numbers you need to use SetPrecision at the very least.