diff --git a/homeassistant/components/alexa/capabilities.py b/homeassistant/components/alexa/capabilities.py
index 660ef46e478..ea8a1ed8681 100644
--- a/homeassistant/components/alexa/capabilities.py
+++ b/homeassistant/components/alexa/capabilities.py
@@ -1535,7 +1535,9 @@ class AlexaRangeController(AlexaCapability):
                 labels=["Percentage", AlexaGlobalCatalog.SETTING_FAN_SPEED],
                 min_value=0,
                 max_value=100,
-                precision=percentage_step if percentage_step else 100,
+                # precision must be a divider of 100 and must be an integer; set step
+                # size to 1 for a consistent behavior except for on/off fans
+                precision=1 if percentage_step else 100,
                 unit=AlexaGlobalCatalog.UNIT_PERCENT,
             )
             return self._resource.serialize_capability_resources()
diff --git a/tests/components/alexa/test_smart_home.py b/tests/components/alexa/test_smart_home.py
index 71123ca27ba..99d43816050 100644
--- a/tests/components/alexa/test_smart_home.py
+++ b/tests/components/alexa/test_smart_home.py
@@ -365,7 +365,7 @@ async def test_fan(hass):
     assert appliance["endpointId"] == "fan#test_1"
     assert appliance["displayCategories"][0] == "FAN"
     assert appliance["friendlyName"] == "Test fan 1"
-    # Alexa.RangeController is added to make a van controllable when no other controllers are available
+    # Alexa.RangeController is added to make a fan controllable when no other controllers are available
     capabilities = assert_endpoint_capabilities(
         appliance,
         "Alexa.RangeController",
@@ -402,6 +402,39 @@ async def test_fan(hass):
     )
 
 
+async def test_fan2(hass):
+    """Test fan discovery with percentage_step."""
+
+    # Test fan discovery with percentage_step
+    device = (
+        "fan.test_2",
+        "on",
+        {
+            "friendly_name": "Test fan 2",
+            "percentage": 66,
+            "supported_features": 1,
+            "percentage_step": 33.3333,
+        },
+    )
+    appliance = await discovery_test(device, hass)
+
+    assert appliance["endpointId"] == "fan#test_2"
+    assert appliance["displayCategories"][0] == "FAN"
+    assert appliance["friendlyName"] == "Test fan 2"
+    # Alexa.RangeController is added to make a fan controllable when no other controllers are available
+    capabilities = assert_endpoint_capabilities(
+        appliance,
+        "Alexa.RangeController",
+        "Alexa.PowerController",
+        "Alexa.EndpointHealth",
+        "Alexa",
+    )
+
+    power_capability = get_capability(capabilities, "Alexa.PowerController")
+    assert "capabilityResources" not in power_capability
+    assert "configuration" not in power_capability
+
+
 async def test_variable_fan(hass):
     """Test fan discovery.