diff --git a/package/CHANGELOG b/package/CHANGELOG
index 7472c476ed..e59f1b068d 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -21,6 +21,8 @@ The rules for this file:
  * 2.8.0
 
 Fixes
+ * Fix doctest errors of analysis/pca.py related to rounding issues 
+   (Issue #3925, PR #4377)
  * Convert openmm Quantity to raw value for KE and PE in OpenMMSimulationReader.
  * Atomname methods can handle empty groups (Issue #2879, PR #4529)
  * Add support for TPR files produced by Gromacs 2024.1 (PR #4523)
diff --git a/package/MDAnalysis/analysis/pca.py b/package/MDAnalysis/analysis/pca.py
index 280f7c2a8d..e4818aabf2 100644
--- a/package/MDAnalysis/analysis/pca.py
+++ b/package/MDAnalysis/analysis/pca.py
@@ -650,10 +650,10 @@ def rmsip(self, other, n_components=None):
             >>> first_interval = pca.PCA(u, select="backbone").run(start=0, stop=25)
             >>> second_interval = pca.PCA(u, select="backbone").run(start=25, stop=50)
             >>> last_interval = pca.PCA(u, select="backbone").run(start=75)
-            >>> first_interval.rmsip(second_interval, n_components=3)
-            0.38147609331128324
-            >>> first_interval.rmsip(last_interval, n_components=3)
-            0.17478244043688052
+            >>> round(first_interval.rmsip(second_interval, n_components=3), 6)
+            0.381476
+            >>> round(first_interval.rmsip(last_interval, n_components=3), 6)
+            0.174782
 
 
         See also
@@ -826,14 +826,14 @@ def rmsip(a, b, n_components=None):
         >>> first_interval = pca.PCA(u, select="backbone").run(start=0, stop=25)
         >>> second_interval = pca.PCA(u, select="backbone").run(start=25, stop=50)
         >>> last_interval = pca.PCA(u, select="backbone").run(start=75)
-        >>> pca.rmsip(first_interval.results.p_components.T,
+        >>> round(pca.rmsip(first_interval.results.p_components.T,
         ...           second_interval.results.p_components.T,
-        ...           n_components=3)
-        0.38147609331128324
-        >>> pca.rmsip(first_interval.results.p_components.T,
+        ...           n_components=3), 6)
+        0.381476
+        >>> round(pca.rmsip(first_interval.results.p_components.T,
         ...           last_interval.results.p_components.T,
-        ...           n_components=3)
-        0.17478244043688052
+        ...           n_components=3), 6)
+        0.174782
 
 
     .. versionadded:: 1.0.0