diff --git a/ngraph/lib/demand.py b/ngraph/lib/demand.py
index 37d094c..a2b06da 100644
--- a/ngraph/lib/demand.py
+++ b/ngraph/lib/demand.py
@@ -1,8 +1,10 @@
 from __future__ import annotations
 
+import math
 from dataclasses import dataclass, field
 from typing import Optional, Tuple
 
+from ngraph.lib.algorithms.base import MIN_FLOW
 from ngraph.lib.flow_policy import FlowPolicy
 from ngraph.lib.graph import NodeID, StrictMultiDiGraph
 
@@ -21,6 +23,16 @@ class Demand:
     flow_policy: Optional[FlowPolicy] = None
     placed_demand: float = field(default=0.0, init=False)
 
+    @staticmethod
+    def _round_float(value: float) -> float:
+        """Round ``value`` to avoid tiny floating point drift."""
+        if math.isfinite(value):
+            rounded = round(value, 12)
+            if abs(rounded) < MIN_FLOW:
+                return 0.0
+            return rounded
+        return value
+
     def __lt__(self, other: Demand) -> bool:
         """
         Compare Demands by their demand_class (priority). A lower demand_class
@@ -94,7 +106,10 @@ def place(
 
         # placed_now is the difference from the old placed_demand
         placed_now = self.flow_policy.placed_demand - self.placed_demand
-        self.placed_demand = self.flow_policy.placed_demand
+        self.placed_demand = self._round_float(self.flow_policy.placed_demand)
         remaining = to_place - placed_now
 
+        placed_now = self._round_float(placed_now)
+        remaining = self._round_float(remaining)
+
         return placed_now, remaining