diff --git a/changelog.d/11217.bugfix b/changelog.d/11217.bugfix
new file mode 100644
index 000000000..67ebb0d0e
--- /dev/null
+++ b/changelog.d/11217.bugfix
@@ -0,0 +1 @@
+Fix a bug introduced in 1.35.0 which made it impossible to join rooms that return a `send_join` response containing floats.
\ No newline at end of file
diff --git a/synapse/federation/transport/client.py b/synapse/federation/transport/client.py
index d96317883..10b5aa5af 100644
--- a/synapse/federation/transport/client.py
+++ b/synapse/federation/transport/client.py
@@ -1310,14 +1310,17 @@ class SendJoinParser(ByteParser[SendJoinResponse]):
         self._coro_state = ijson.items_coro(
             _event_list_parser(room_version, self._response.state),
             prefix + "state.item",
+            use_float=True,
         )
         self._coro_auth = ijson.items_coro(
             _event_list_parser(room_version, self._response.auth_events),
             prefix + "auth_chain.item",
+            use_float=True,
         )
         self._coro_event = ijson.kvitems_coro(
             _event_parser(self._response.event_dict),
             prefix + "org.matrix.msc3083.v2.event",
+            use_float=True,
         )
 
     def write(self, data: bytes) -> int: