diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index d5bea84..c708101 100644
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -1349,7 +1349,17 @@ Internally, the underlying CLN is responsible for this behavior and we
 refer the reader to CLN's documentation.  Suffice to say that
 the same behavior applies to complex numbers as well as return values of
 certain functions.  Complex numbers are automatically converted to real
-numbers if the imaginary part becomes zero.  The full set of tests that
+numbers if the imaginary part becomes zero as an exact number.
+Complex numbers with an imaginary part equal to zero as a floating point number
+are not converted automatically to real numbers.
+The reason is the following: Comparing two real floating point numbers for equality
+gives only the information that they are represented by the same rational number
+within a given precision.
+Thus, if the imaginary part is equal to zero as a floating point number we only know
+that it is smaller than a given precision.
+Of course, in such a case a user can always convert the number explicitly to a real number,
+it is just not done automatically.
+The full set of tests that
 can be applied is listed in the following table.
 
 @cartouche