diff --git a/Doc/library/functions.rst b/Doc/library/functions.rst
index 817c1f858aa..2e988257d5d 100644
--- a/Doc/library/functions.rst
+++ b/Doc/library/functions.rst
@@ -650,20 +650,23 @@ are always available.  They are listed here in alphabetical order.
    sign may be ``'+'`` or ``'-'``; a ``'+'`` sign has no effect on the value
    produced.  The argument may also be a string representing a NaN
    (not-a-number), or positive or negative infinity.  More precisely, the
-   input must conform to the following grammar after leading and trailing
-   whitespace characters are removed:
+   input must conform to the ``floatvalue`` production rule in the following
+   grammar, after leading and trailing whitespace characters are removed:
 
    .. productionlist:: float
       sign: "+" | "-"
       infinity: "Infinity" | "inf"
       nan: "nan"
-      numeric_value: `floatnumber` | `infinity` | `nan`
-      numeric_string: [`sign`] `numeric_value`
+      digitpart: `digit` (["_"] `digit`)*
+      number: [`digitpart`] "." `digitpart` | `digitpart` ["."]
+      exponent: ("e" | "E") ["+" | "-"] `digitpart`
+      floatnumber: number [`exponent`]
+      floatvalue: [`sign`] (`floatnumber` | `infinity` | `nan`)
 
-   Here ``floatnumber`` is the form of a Python floating-point literal,
-   described in :ref:`floating`.  Case is not significant, so, for example,
-   "inf", "Inf", "INFINITY", and "iNfINity" are all acceptable spellings for
-   positive infinity.
+   Here ``digit`` is a Unicode decimal digit (character in the Unicode general
+   category ``Nd``). Case is not significant, so, for example, "inf", "Inf",
+   "INFINITY", and "iNfINity" are all acceptable spellings for positive
+   infinity.
 
    Otherwise, if the argument is an integer or a floating point number, a
    floating point number with the same value (within Python's floating point