Fix issue #63444, sorry first time if I did something wrong

doc/source/whatsnew/v3.0.0.rst

@@ -1453,7 +1453,7 @@ Other
   array if the array shares data with the original DataFrame or Series (:ref:`copy_on_write_read_only_na`).
   This logic is expanded to accessing the underlying pandas ExtensionArray
   through ``.array`` (or ``.values`` depending on the dtype) as well (:issue:`61925`).
-
+- Bug in :meth:`Series.round` where series shows TypeError when passed empty Series (:issue:`63444`)
 .. ***DO NOT USE THIS SECTION***
 
 .. ---------------------------------------------------------------------------

pandas/core/series.py

@@ -2579,8 +2579,11 @@ def round(self, decimals: int = 0, *args, **kwargs) -> Series:
         dtype: float64
         """
         nv.validate_round(args, kwargs)
-        if self.dtype == "object":
+        if not self.empty and (self.dtype == "object" or self.dtype == "str"):
             raise TypeError("Expected numeric dtype, got object instead.")
+        if not self.empty and (self.dtype == "str"):
+            raise TypeError("Expected numeric dtype, got string instead.")
+
         new_mgr = self._mgr.round(decimals=decimals)
         return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
             self, method="round"

pandas/tests/series/methods/test_round_empty.py

@@ -0,0 +1,40 @@
+import pytest
+
+import pandas as pd
+import pandas.testing as tm
+
+# GH63444
+
+
+def test_series_round_empty1():
+    result = pd.Series([]).round(2)
+    expected = pd.Series([])
+    tm.assert_series_equal(result, expected)
+
+
+def test_series_round_empty2():
+    result = pd.Series([], dtype="float64").round()
+    expected = pd.Series([], dtype="float64")
+    tm.assert_series_equal(result, expected)
+
+
+def test_series_round_numeric():
+    result = pd.Series([1.2345, 2.6789, 3.14159]).round(2)
+    expected = pd.Series([1.23, 2.68, 3.14])
+    tm.assert_series_equal(result, expected)
+
+
+def test_series_round_integers():
+    result = pd.Series([1, 2, 3]).round(2)
+    expected = pd.Series([1, 2, 3])
+    tm.assert_series_equal(result, expected)
+
+
+def test_series_round_str():
+    with pytest.raises(TypeError):
+        pd.Series(["a", "b", "c"]).round(2)
+
+
+def test_series_round_obj():
+    with pytest.raises(TypeError):
+        pd.Series(["123"], dtype="object").round(2)