diff --git a/pandas/core/arrays/string_arrow.py b/pandas/core/arrays/string_arrow.py
index 219c52c4a65b9..a6835ab1325a0 100644
--- a/pandas/core/arrays/string_arrow.py
+++ b/pandas/core/arrays/string_arrow.py
@@ -31,14 +31,17 @@
 from pandas.util._decorators import doc
 from pandas.util._validators import validate_fillna_kwargs
 
+from pandas.core.dtypes.base import ExtensionDtype
 from pandas.core.dtypes.common import (
     is_array_like,
     is_bool_dtype,
+    is_dtype_equal,
     is_integer,
     is_integer_dtype,
     is_object_dtype,
     is_scalar,
     is_string_dtype,
+    pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import register_extension_dtype
 from pandas.core.dtypes.missing import isna
@@ -48,6 +51,7 @@
 from pandas.core.arrays.base import ExtensionArray
 from pandas.core.arrays.boolean import BooleanDtype
 from pandas.core.arrays.integer import Int64Dtype
+from pandas.core.arrays.numeric import NumericDtype
 from pandas.core.arrays.string_ import StringDtype
 from pandas.core.indexers import (
     check_array_indexer,
@@ -290,10 +294,14 @@ def to_numpy(  # type: ignore[override]
         """
         # TODO: copy argument is ignored
 
-        if na_value is lib.no_default:
-            na_value = self._dtype.na_value
-        result = self._data.__array__(dtype=dtype)
-        result[isna(result)] = na_value
+        result = np.array(self._data, dtype=dtype)
+        if self._data.null_count > 0:
+            if na_value is lib.no_default:
+                if dtype and np.issubdtype(dtype, np.floating):
+                    return result
+                na_value = self._dtype.na_value
+            mask = self.isna()
+            result[mask] = na_value
         return result
 
     def __len__(self) -> int:
@@ -737,6 +745,24 @@ def value_counts(self, dropna: bool = True) -> Series:
 
         return Series(counts, index=index).astype("Int64")
 
+    def astype(self, dtype, copy=True):
+        dtype = pandas_dtype(dtype)
+
+        if is_dtype_equal(dtype, self.dtype):
+            if copy:
+                return self.copy()
+            return self
+
+        elif isinstance(dtype, NumericDtype):
+            data = self._data.cast(pa.from_numpy_dtype(dtype.numpy_dtype))
+            return dtype.__from_arrow__(data)
+
+        elif isinstance(dtype, ExtensionDtype):
+            cls = dtype.construct_array_type()
+            return cls._from_sequence(self, dtype=dtype, copy=copy)
+
+        return super().astype(dtype, copy)
+
     # ------------------------------------------------------------------------
     # String methods interface
 
diff --git a/pandas/tests/arrays/string_/test_string.py b/pandas/tests/arrays/string_/test_string.py
index e3b43c544a477..c9533e239abe0 100644
--- a/pandas/tests/arrays/string_/test_string.py
+++ b/pandas/tests/arrays/string_/test_string.py
@@ -3,6 +3,8 @@
 Tests for the str accessors are in pandas/tests/strings/test_string_array.py
 """
 
+import re
+
 import numpy as np
 import pytest
 
@@ -325,12 +327,19 @@ def test_from_sequence_no_mutate(copy, cls, request):
     tm.assert_numpy_array_equal(nan_arr, expected)
 
 
-def test_astype_int(dtype, request):
-    if dtype == "arrow_string":
-        reason = "Cannot interpret 'Int64Dtype()' as a data type"
-        mark = pytest.mark.xfail(raises=TypeError, reason=reason)
-        request.node.add_marker(mark)
+def test_astype_int(dtype):
+    arr = pd.array(["1", "2", "3"], dtype=dtype)
+    result = arr.astype("int64")
+    expected = np.array([1, 2, 3], dtype="int64")
+    tm.assert_numpy_array_equal(result, expected)
+
+    arr = pd.array(["1", pd.NA, "3"], dtype=dtype)
+    msg = re.escape("int() argument must be a string, a bytes-like object or a number")
+    with pytest.raises(TypeError, match=msg):
+        arr.astype("int64")
+
 
+def test_astype_nullable_int(dtype):
     arr = pd.array(["1", pd.NA, "3"], dtype=dtype)
 
     result = arr.astype("Int64")
@@ -338,19 +347,9 @@ def test_astype_int(dtype, request):
     tm.assert_extension_array_equal(result, expected)
 
 
-def test_astype_float(dtype, any_float_allowed_nullable_dtype, request):
+def test_astype_float(dtype, any_float_allowed_nullable_dtype):
     # Don't compare arrays (37974)
-
-    if dtype == "arrow_string":
-        if any_float_allowed_nullable_dtype in {"Float32", "Float64"}:
-            reason = "Cannot interpret 'Float32Dtype()' as a data type"
-        else:
-            reason = "float() argument must be a string or a number, not 'NAType'"
-        mark = pytest.mark.xfail(raises=TypeError, reason=reason)
-        request.node.add_marker(mark)
-
     ser = pd.Series(["1.1", pd.NA, "3.3"], dtype=dtype)
-
     result = ser.astype(any_float_allowed_nullable_dtype)
     expected = pd.Series([1.1, np.nan, 3.3], dtype=any_float_allowed_nullable_dtype)
     tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_astype.py b/pandas/tests/series/methods/test_astype.py
index bebe6948cff9c..ffaecf1576364 100644
--- a/pandas/tests/series/methods/test_astype.py
+++ b/pandas/tests/series/methods/test_astype.py
@@ -379,7 +379,9 @@ class TestAstypeString:
             # currently no way to parse IntervalArray from a list of strings
         ],
     )
-    def test_astype_string_to_extension_dtype_roundtrip(self, data, dtype, request):
+    def test_astype_string_to_extension_dtype_roundtrip(
+        self, data, dtype, request, nullable_string_dtype
+    ):
         if dtype == "boolean" or (
             dtype in ("period[M]", "datetime64[ns]", "timedelta64[ns]") and NaT in data
         ):
@@ -389,7 +391,8 @@ def test_astype_string_to_extension_dtype_roundtrip(self, data, dtype, request):
             request.node.add_marker(mark)
         # GH-40351
         s = Series(data, dtype=dtype)
-        tm.assert_series_equal(s, s.astype("string").astype(dtype))
+        result = s.astype(nullable_string_dtype).astype(dtype)
+        tm.assert_series_equal(result, s)
 
 
 class TestAstypeCategorical: