diff --git a/news/update_tests.rst b/news/update_tests.rst
new file mode 100644
index 00000000..790d30b1
--- /dev/null
+++ b/news/update_tests.rst
@@ -0,0 +1,23 @@
+**Added:**
+
+* <news item>
+
+**Changed:**
+
+* <news item>
+
+**Deprecated:**
+
+* <news item>
+
+**Removed:**
+
+* <news item>
+
+**Fixed:**
+
+* <news item>
+
+**Security:**
+
+* <news item>
diff --git a/tests/test_morphio.py b/tests/test_morphio.py
index b16d414a..08699dcb 100644
--- a/tests/test_morphio.py
+++ b/tests/test_morphio.py
@@ -50,6 +50,20 @@ def isfloat(s):
     return False
 
 
+def are_files_same(file1, file2):
+    """Assert that two files have (approximately) the same numerical
+    values."""
+    for f1_row, f2_row in zip(file1, file2):
+        f1_arr = f1_row.split()
+        f2_arr = f2_row.split()
+        assert len(f1_arr) == len(f2_arr)
+        for idx, _ in enumerate(f1_arr):
+            if isfloat(f1_arr[idx]) and isfloat(f2_arr[idx]):
+                assert np.isclose(float(f1_arr[idx]), float(f2_arr[idx]))
+            else:
+                assert f1_arr[idx] == f2_arr[idx]
+
+
 class TestApp:
     @pytest.fixture
     def setup(self):
@@ -106,9 +120,9 @@ def test_morph_outputs(self, setup, tmp_path):
         for file in common:
             with open(tmp_succinct.joinpath(file)) as gf:
                 with open(test_saving_succinct.joinpath(file)) as tf:
-                    generated = filter(ignore_path, gf)
-                    target = filter(ignore_path, tf)
-                    assert all(x == y for x, y in zip(generated, target))
+                    actual = filter(ignore_path, gf)
+                    expected = filter(ignore_path, tf)
+                    are_files_same(actual, expected)
 
         # Save multiple verbose morphs
         tmp_verbose = tmp_path.joinpath("verbose")
@@ -147,9 +161,9 @@ def test_morph_outputs(self, setup, tmp_path):
         for file in common:
             with open(tmp_verbose.joinpath(file)) as gf:
                 with open(test_saving_verbose.joinpath(file)) as tf:
-                    generated = filter(ignore_path, gf)
-                    target = filter(ignore_path, tf)
-                    assert all(x == y for x, y in zip(generated, target))
+                    actual = filter(ignore_path, gf)
+                    expected = filter(ignore_path, tf)
+                    are_files_same(actual, expected)
 
     def test_morphsqueeze_outputs(self, setup, tmp_path):
         # The file squeeze_morph has a squeeze and stretch applied
@@ -182,19 +196,9 @@ def test_morphsqueeze_outputs(self, setup, tmp_path):
         # Check squeeze morph generates the correct output
         with open(sqr) as mf:
             with open(target_file) as tf:
-                morphed = filter(ignore_path, mf)
-                target = filter(ignore_path, tf)
-                for m, t in zip(morphed, target):
-                    m_row = m.split()
-                    t_row = t.split()
-                    assert len(m_row) == len(t_row)
-                    for idx, _ in enumerate(m_row):
-                        if isfloat(m_row[idx]) and isfloat(t_row[idx]):
-                            assert np.isclose(
-                                float(m_row[idx]), float(t_row[idx])
-                            )
-                        else:
-                            assert m_row[idx] == t_row[idx]
+                actual = filter(ignore_path, mf)
+                expected = filter(ignore_path, tf)
+                are_files_same(actual, expected)
 
     def test_morphfuncy_outputs(self, tmp_path):
         def quadratic(x, y, a0, a1, a2):
@@ -215,16 +219,6 @@ def quadratic(x, y, a0, a1, a2):
 
         with open(testdata_dir.joinpath("funcy_target.cgr")) as tf:
             with open(tmp_path.joinpath("funcy_target.cgr")) as gf:
-                generated = filter(ignore_path, gf)
-                target = filter(ignore_path, tf)
-                for m, t in zip(generated, target):
-                    m_row = m.split()
-                    t_row = t.split()
-                    assert len(m_row) == len(t_row)
-                    for idx, _ in enumerate(m_row):
-                        if isfloat(m_row[idx]) and isfloat(t_row[idx]):
-                            assert np.isclose(
-                                float(m_row[idx]), float(t_row[idx])
-                            )
-                        else:
-                            assert m_row[idx] == t_row[idx]
+                actual = filter(ignore_path, gf)
+                expected = filter(ignore_path, tf)
+                are_files_same(actual, expected)
diff --git a/tests/test_morphpy.py b/tests/test_morphpy.py
index 848fe1a9..0a288271 100644
--- a/tests/test_morphpy.py
+++ b/tests/test_morphpy.py
@@ -91,7 +91,14 @@ class Chain:
             assert np.allclose(
                 [rw], [self.morphapp_results[target_file.name]["Rw"]]
             )
-        assert morph_results == self.morphapp_results
+        # Check values in dictionaries are approximately equal
+        for file in morph_results.keys():
+            morph_params = morph_results[file]
+            morphapp_params = self.morphapp_results[file]
+            for key in morph_params.keys():
+                assert morph_params[key] == pytest.approx(
+                    morphapp_params[key], abs=1e-08
+                )
 
     def test_morphpy(self, setup_morph):
         morph_results = {}
@@ -113,7 +120,14 @@ class Chain:
             assert np.allclose(
                 [rw], [self.morphapp_results[target_file.name]["Rw"]]
             )
-        assert morph_results == self.morphapp_results
+            # Check values in dictionaries are approximately equal
+            for file in morph_results.keys():
+                morph_params = morph_results[file]
+                morphapp_params = self.morphapp_results[file]
+                for key in morph_params.keys():
+                    assert morph_params[key] == pytest.approx(
+                        morphapp_params[key], abs=1e-08
+                    )
 
     def test_morphfuncy(self, setup_morph):
         def gaussian(x, mu, sigma):