Limit precision when stringifying float states (#48822)

* Limit precision when stringifying float states

* Add test

* Fix typing

* Move StateType

* Update

* Move conversion to entity helper

* Address review comments

* Tweak precision

* Tweak

* Make _stringify_state an instance method

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