diff --git a/homeassistant/helpers/entity.py b/homeassistant/helpers/entity.py
index e6af7751c88..1706d9b309d 100644
--- a/homeassistant/helpers/entity.py
+++ b/homeassistant/helpers/entity.py
@@ -7,6 +7,8 @@ from collections.abc import Awaitable, Iterable, Mapping
 from datetime import datetime, timedelta
 import functools as ft
 import logging
+import math
+import sys
 from timeit import default_timer as timer
 from typing import Any
 
@@ -43,6 +45,10 @@ DATA_ENTITY_SOURCE = "entity_info"
 SOURCE_CONFIG_ENTRY = "config_entry"
 SOURCE_PLATFORM_CONFIG = "platform_config"
 
+# Used when converting float states to string: limit precision according to machine
+# epsilon to make the string representation readable
+FLOAT_PRECISION = abs(int(math.floor(math.log10(abs(sys.float_info.epsilon))))) - 1
+
 
 @callback
 @bind_hass
@@ -327,6 +333,19 @@ class Entity(ABC):
 
         self._async_write_ha_state()
 
+    def _stringify_state(self) -> str:
+        """Convert state to string."""
+        if not self.available:
+            return STATE_UNAVAILABLE
+        state = self.state
+        if state is None:
+            return STATE_UNKNOWN
+        if isinstance(state, float):
+            # If the entity's state is a float, limit precision according to machine
+            # epsilon to make the string representation readable
+            return f"{state:.{FLOAT_PRECISION}}"
+        return str(state)
+
     @callback
     def _async_write_ha_state(self) -> None:
         """Write the state to the state machine."""
@@ -346,11 +365,8 @@ class Entity(ABC):
         attr = self.capability_attributes
         attr = dict(attr) if attr else {}
 
-        if not self.available:
-            state = STATE_UNAVAILABLE
-        else:
-            sstate = self.state
-            state = STATE_UNKNOWN if sstate is None else str(sstate)
+        state = self._stringify_state()
+        if self.available:
             attr.update(self.state_attributes or {})
             extra_state_attributes = self.extra_state_attributes
             # Backwards compatibility for "device_state_attributes" deprecated in 2021.4
diff --git a/tests/components/input_number/test_init.py b/tests/components/input_number/test_init.py
index d6d80a9ad87..ca496723d99 100644
--- a/tests/components/input_number/test_init.py
+++ b/tests/components/input_number/test_init.py
@@ -162,6 +162,26 @@ async def test_increment(hass):
     assert float(state.state) == 51
 
 
+async def test_rounding(hass):
+    """Test increment introducing floating point error is rounded."""
+    assert await async_setup_component(
+        hass,
+        DOMAIN,
+        {DOMAIN: {"test_2": {"initial": 2.4, "min": 0, "max": 51, "step": 1.2}}},
+    )
+    entity_id = "input_number.test_2"
+    assert 2.4 + 1.2 != 3.6
+
+    state = hass.states.get(entity_id)
+    assert float(state.state) == 2.4
+
+    await increment(hass, entity_id)
+    await hass.async_block_till_done()
+
+    state = hass.states.get(entity_id)
+    assert float(state.state) == 3.6
+
+
 async def test_decrement(hass):
     """Test decrement method."""
     assert await async_setup_component(
diff --git a/tests/helpers/test_entity.py b/tests/helpers/test_entity.py
index 8d587301fb8..8142f563f01 100644
--- a/tests/helpers/test_entity.py
+++ b/tests/helpers/test_entity.py
@@ -774,3 +774,17 @@ async def test_get_supported_features_raises_on_unknown(hass):
     """Test get_supported_features raises on unknown entity_id."""
     with pytest.raises(HomeAssistantError):
         entity.get_supported_features(hass, "hello.world")
+
+
+async def test_float_conversion(hass):
+    """Test conversion of float state to string rounds."""
+    assert 2.4 + 1.2 != 3.6
+    with patch.object(entity.Entity, "state", PropertyMock(return_value=2.4 + 1.2)):
+        ent = entity.Entity()
+        ent.hass = hass
+        ent.entity_id = "hello.world"
+        ent.async_write_ha_state()
+
+    state = hass.states.get("hello.world")
+    assert state is not None
+    assert state.state == "3.6"