diff --git a/crates/ailang-surface/src/parse.rs b/crates/ailang-surface/src/parse.rs
index fd884a7..1b5753b 100644
--- a/crates/ailang-surface/src/parse.rs
+++ b/crates/ailang-surface/src/parse.rs
@@ -162,6 +162,7 @@ fn tok_label(t: &Tok) -> String {
         Tok::LParen => "`(`".into(),
         Tok::RParen => "`)`".into(),
         Tok::Int(v) => format!("integer `{v}`"),
+        Tok::Float(bits) => format!("float `0x{bits:016x}`"),
         Tok::Str(s) => format!("string {s:?}"),
         Tok::Ident(s) => format!("ident `{s}`"),
     }
@@ -1233,6 +1234,10 @@ impl<'a> Parser<'a> {
                 self.cur += 1;
                 Ok(Term::Lit { lit: Literal::Int { value: v } })
             }
+            Some(Token { tok: Tok::Float(bits), .. }) => {
+                self.cur += 1;
+                Ok(Term::Lit { lit: Literal::Float { bits } })
+            }
             Some(Token { tok: Tok::Str(s), .. }) => {
                 self.cur += 1;
                 Ok(Term::Lit { lit: Literal::Str { value: s } })
@@ -1627,6 +1632,10 @@ impl<'a> Parser<'a> {
                 self.cur += 1;
                 Literal::Int { value: v }
             }
+            Some(Token { tok: Tok::Float(bits), .. }) => {
+                self.cur += 1;
+                Literal::Float { bits }
+            }
             Some(Token { tok: Tok::Str(s), .. }) => {
                 self.cur += 1;
                 Literal::Str { value: s }
@@ -1640,7 +1649,7 @@ impl<'a> Parser<'a> {
                     Literal::Bool { value: false }
                 } else {
                     return Err(ParseError::Unexpected {
-                        expected: "literal form (integer, string, `true`, or `false`)".into(),
+                        expected: "literal form (integer, float, string, `true`, or `false`)".into(),
                         got: tok_label(&Tok::Ident(s)),
                         pos: span.start,
                     });
@@ -1648,7 +1657,7 @@ impl<'a> Parser<'a> {
             }
             Some(t) => {
                 return Err(ParseError::Unexpected {
-                    expected: "literal form (integer, string, `true`, or `false`)".into(),
+                    expected: "literal form (integer, float, string, `true`, or `false`)".into(),
                     got: tok_label(&t.tok),
                     pos: t.span.start,
                 });
@@ -2403,4 +2412,20 @@ mod tests {
             "expected duplicate-doc diagnostic, got: {msg}"
         );
     }
+
+    /// Floats milestone iter 2.2 RED: `1.5` parses as
+    /// `Term::Lit { lit: Literal::Float { bits: 0x3ff8_0000_0000_0000 } }`.
+    /// Property protected: a `Tok::Float` produced by the lexer flows through
+    /// `parse_term` into a `Literal::Float` AST node carrying the same bit
+    /// pattern, so the surface→AST translation is bit-exact.
+    #[test]
+    fn parses_float_atom_term() {
+        let t = parse_term("1.5").expect("parse term");
+        match t {
+            Term::Lit { lit: Literal::Float { bits } } => {
+                assert_eq!(bits, 0x3ff8_0000_0000_0000u64);
+            }
+            other => panic!("expected Term::Lit::Float, got {other:?}"),
+        }
+    }
 }