diff --git a/pep-0680.rst b/pep-0680.rst
index e10958233..cd688916b 100644
--- a/pep-0680.rst
+++ b/pep-0680.rst
@@ -333,14 +333,17 @@ support could be added later in a backward-compatible way.
 Removing support for ``parse_float`` in ``tomllib.load[s]``
 -----------------------------------------------------------
 
-This option is not strictly necessary, since TOML floats are "IEEE 754 binary64
-values", which is equivalent to a Python ``float`` on most architectures.
-However, parsing floats differently, such as to ``decimal.Decimal``, allows
-users extra precision beyond that promised by the TOML format. In the
-author of ``tomli``'s experience, this is particularly useful in scientific and
-financial applications. This is also useful for other cases that need greater
-precision, or where end-users include non-developers who may not be aware of
-the limits of binary64 floats.
+This option is not strictly necessary, since TOML floats should be implemented
+as "IEEE 754 binary64 values", which is equivalent to a Python ``float`` on most
+architectures.
+
+The TOML specification uses the word "SHOULD", however, implying a
+recommendation that can be ignored for valid reasons. Parsing floats
+differently, such as to ``decimal.Decimal``, allows users extra precision beyond
+that promised by the TOML format. In the author of ``tomli``'s experience, this
+is particularly useful in scientific and financial applications. This is also
+useful for other cases that need greater precision, or where end-users include
+non-developers who may not be aware of the limits of binary64 floats.
 
 There are also niche architectures where the Python ``float`` is not a IEEE 754
 binary64 value. The ``parse_float`` argument allows users to achieve correct