Create formatting wrapper for use with ToString

Question

I'd like to create a custom number format for use with ToString. However if I do the obvious and create a function that calls NumberForm with modified options:

numberform = 
  NumberForm[#, 
    ExponentFunction -> (If[-5 < # < 5, Null, #]&), 
    NumberFormat -> (If[#3 != "", SequenceForm[#1, "E", #3],#1]&)]&  

Slot[1]&

It works fine as a function:

numberform[1234567890.]  

1.23457E9

but not with ToString:

ToString[1234567890., numberform]  

ToString[1.23457*10^9, Slot[1]&]

Is there some attribute I have to set to make it behave like the built-in forms? Is that even possible? Is there a workaround?

Answer 1

You can use TagSet (/:). This attaches the definition to numberform instead of ToString:

ClearAll[numberform];
numberformFunction = 
  NumberForm[#, ExponentFunction -> (If[-5 < # < 5, Null, #] &), 
    NumberFormat -> (If[#3 != "", 
    SequenceForm[#1, "E", #3], #1] &)] &;
numberform /: ToString[s_, numberform] := numberformFunction@s;
ToString[1234567890., numberform]

1.23457E9

Answer 2

Why not simply

numberform = 
 NumberForm[ToExpression@#, 
   ExponentFunction -> (If[-5 < # < 5, Null, #] &), 
   NumberFormat -> (If[#3 != "", SequenceForm[#1, "E", #3], #1] &)] &

???

numberform[ToString@123456.]

1.23456E5

numberform[123456.]

1.23456E5