diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index b4cc71a25792f..5c79942efb908 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -14,6 +14,7 @@
 from pandas.core.dtypes.common import (
     ensure_platform_int,
     ensure_python_int,
+    is_float,
     is_integer,
     is_integer_dtype,
     is_list_like,
@@ -344,12 +345,14 @@ def __contains__(self, key: Union[int, np.integer]) -> bool:
 
     @Appender(_index_shared_docs["get_loc"])
     def get_loc(self, key, method=None, tolerance=None):
-        if is_integer(key) and method is None and tolerance is None:
-            new_key = int(key)
-            try:
-                return self._range.index(new_key)
-            except ValueError:
-                raise KeyError(key)
+        if method is None and tolerance is None:
+            if is_integer(key) or (is_float(key) and key.is_integer()):
+                new_key = int(key)
+                try:
+                    return self._range.index(new_key)
+                except ValueError:
+                    raise KeyError(key)
+            raise KeyError(key)
         return super().get_loc(key, method=method, tolerance=tolerance)
 
     @Appender(_index_shared_docs["get_indexer"])
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index 8d98ab18963b6..0e5d1d45ad6db 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -735,8 +735,9 @@ def test_engineless_lookup(self):
 
         assert "_engine" not in idx._cache
 
-        # The engine is still required for lookup of a different dtype scalar:
+        # Different types of scalars can be excluded immediately, no need to
+        #  use the _engine
         with pytest.raises(KeyError, match="'a'"):
-            assert idx.get_loc("a") == -1
+            idx.get_loc("a")
 
-        assert "_engine" in idx._cache
+        assert "_engine" not in idx._cache