Albert,

To enter any number to a specific precision you can use a shortcut: entering 0.5`30 will give you 0.5 with 30 digits of precision. The prime is the character above the Tab key.

Unless you specifically specify the precision, as soon as you enter a decimal point you are using machine precision. That is why using 1/2 instead of 0.5 will maintain the expression with infinite precision until you either use N[] to truncate it or mix it with some real numbers with decimal points.

Regards,

Neil

It's not a unexplained behavior it is a normal behavior (not a bug).

phi1 = (1 + Sqrt[5])/2; N[phi1, 20] 
phi2 = (1 + 5^(1/2))/2; N[phi2, 20] 
phi3 = (1 + 5^(SetPrecision[0.5, 20]))/2; N[phi3, 20] 

(* 1.6180339887498948482 *)
(* 1.6180339887498948482 *)
(* 1.6180339887498948482 *)

because:

{Precision[(1 + 5^(.5))/2], Precision[(1 + 5^(1/2))/2]}

(* {MachinePrecision, \[Infinity]} *)

This is very well explained in this book