diff --git a/cirq-core/cirq/ops/common_gates.py b/cirq-core/cirq/ops/common_gates.py
index 133de6dc9cf..237a6ec75f2 100644
--- a/cirq-core/cirq/ops/common_gates.py
+++ b/cirq-core/cirq/ops/common_gates.py
@@ -285,7 +285,7 @@ def _phase_by_(self, phase_turns, qubit_index):
     def _has_stabilizer_effect_(self) -> bool | None:
         if self._is_parameterized_() or self._dimension != 2:
             return None
-        return self.exponent % 0.5 == 0
+        return abs(self.exponent % 0.5) < 1e-8
 
     def __str__(self) -> str:
         if self._global_shift == 0:
@@ -480,7 +480,7 @@ def _phase_by_(self, phase_turns, qubit_index):
     def _has_stabilizer_effect_(self) -> bool | None:
         if self._is_parameterized_():
             return None
-        return self.exponent % 0.5 == 0
+        return abs(self.exponent % 0.5) < 1e-8
 
     def __str__(self) -> str:
         if self._global_shift == 0:
@@ -760,7 +760,7 @@ def _phase_by_(self, phase_turns: float, qubit_index: int):
     def _has_stabilizer_effect_(self) -> bool | None:
         if self._is_parameterized_() or self._dimension != 2:
             return None
-        return self.exponent % 0.5 == 0
+        return abs(self.exponent % 0.5) < 1e-8
 
     def _circuit_diagram_info_(
         self, args: cirq.CircuitDiagramInfoArgs