diff --git a/src/Avalonia.Base/Layout/LayoutHelper.cs b/src/Avalonia.Base/Layout/LayoutHelper.cs
index 404d19906a..0851dbaea9 100644
--- a/src/Avalonia.Base/Layout/LayoutHelper.cs
+++ b/src/Avalonia.Base/Layout/LayoutHelper.cs
@@ -251,6 +251,17 @@ namespace Avalonia.Layout
         {
             double newValue;
 
+            // Round the value to avoid FP errors. This is needed because if `value` has a floating
+            // point precision error (e.g. 79.333333333333343) then when it's multiplied by
+            // `dpiScale` and rounded up, it will be rounded up to a value one greater than it
+            // should be.
+#if NET6_0_OR_GREATER
+            value = Math.Round(value, 8, MidpointRounding.ToZero);
+#else
+            // MidpointRounding.ToZero isn't available in netstandard2.0.
+            value = Math.Truncate(value * 1e8) / 1e8;
+#endif
+
             // If DPI == 1, don't use DPI-aware rounding.
             if (!MathUtilities.IsOne(dpiScale))
             {
diff --git a/src/Avalonia.Controls.ColorPicker/Converters/DoNothingForNullConverter.cs b/src/Avalonia.Controls.ColorPicker/Converters/DoNothingForNullConverter.cs
new file mode 100644
index 0000000000..421a5acb28
--- /dev/null
+++ b/src/Avalonia.Controls.ColorPicker/Converters/DoNothingForNullConverter.cs
@@ -0,0 +1,35 @@
+using System;
+using System.Globalization;
+using Avalonia.Data;
+using Avalonia.Data.Converters;
+
+namespace Avalonia.Controls.Converters
+{
+    /// <summary>
+    /// Converter that will do nothing (not update bound values) when a null value is encountered.
+    /// This converter enables binding nullable with non-nullable properties in some scenarios.
+    /// </summary>
+    public class DoNothingForNullConverter : IValueConverter
+    {
+        /// <inheritdoc/>
+        public object? Convert(
+            object? value,
+            Type targetType,
+            object? parameter,
+            CultureInfo culture)
+        {
+            return value ?? BindingOperations.DoNothing;
+        }
+
+        /// <inheritdoc/>
+        public object? ConvertBack(
+            object? value,
+            Type targetType,
+            object? parameter,
+            CultureInfo culture)
+        {
+            return value ?? BindingOperations.DoNothing;
+        }
+    }
+}
+
diff --git a/src/Avalonia.Controls.ColorPicker/Themes/Fluent/ColorView.xaml b/src/Avalonia.Controls.ColorPicker/Themes/Fluent/ColorView.xaml
index 59cc48975f..dab4142001 100644
--- a/src/Avalonia.Controls.ColorPicker/Themes/Fluent/ColorView.xaml
+++ b/src/Avalonia.Controls.ColorPicker/Themes/Fluent/ColorView.xaml
@@ -11,6 +11,7 @@
   <pc:ThirdComponentConverter x:Key="ThirdComponentConverter" />
   <converters:ColorToDisplayNameConverter x:Key="ColorToDisplayNameConverter" />
   <converters:ColorToHexConverter x:Key="ColorToHexConverter" />
+  <converters:DoNothingForNullConverter x:Key="DoNothingForNullConverter" />
   <globalization:NumberFormatInfo x:Key="ColorViewComponentNumberFormat" NumberDecimalDigits="0" />
   <x:Double x:Key="ColorViewTabStripHeight">48</x:Double>
   <x:Double x:Key="ColorViewComponentLabelWidth">30</x:Double>
@@ -205,7 +206,7 @@
                 </Border>
               </TabItem.Header>
               <ListBox Items="{TemplateBinding PaletteColors}"
-                       SelectedItem="{Binding Color, RelativeSource={RelativeSource TemplatedParent}, Mode=TwoWay}"
+                       SelectedItem="{Binding Color, RelativeSource={RelativeSource TemplatedParent}, Converter={StaticResource DoNothingForNullConverter}, Mode=TwoWay}"
                        UseLayoutRounding="False"
                        Margin="12">
                 <ListBox.Styles>
diff --git a/src/Avalonia.Controls/Utils/BorderRenderHelper.cs b/src/Avalonia.Controls/Utils/BorderRenderHelper.cs
index ecc7cd98bb..eb9f38894d 100644
--- a/src/Avalonia.Controls/Utils/BorderRenderHelper.cs
+++ b/src/Avalonia.Controls/Utils/BorderRenderHelper.cs
@@ -61,7 +61,7 @@ namespace Avalonia.Controls.Utils
                     _backgroundGeometryCache = null;
                 }
 
-                if (boundRect.Width != 0 && innerRect.Height != 0)
+                if (boundRect.Width != 0 && boundRect.Height != 0)
                 {
                     var borderGeometryKeypoints =
                         new BorderGeometryKeypoints(boundRect, borderThickness, cornerRadius, false);
diff --git a/tests/Avalonia.Controls.UnitTests/BorderTests.cs b/tests/Avalonia.Controls.UnitTests/BorderTests.cs
index 7af7d1cee2..e9ddc8e8a3 100644
--- a/tests/Avalonia.Controls.UnitTests/BorderTests.cs
+++ b/tests/Avalonia.Controls.UnitTests/BorderTests.cs
@@ -78,7 +78,7 @@ namespace Avalonia.Controls.UnitTests
                     }
                 };
 
-                var root = CreatedRoot(1.5, target);
+                var root = CreateRoot(1.5, target);
 
                 root.LayoutManager.ExecuteInitialLayoutPass();
 
@@ -101,7 +101,7 @@ namespace Avalonia.Controls.UnitTests
                     }
                 };
 
-                var root = CreatedRoot(1.5, target);
+                var root = CreateRoot(1.5, target);
 
                 root.LayoutManager.ExecuteInitialLayoutPass();
 
@@ -111,7 +111,58 @@ namespace Avalonia.Controls.UnitTests
                 Assert.Equal(new Size(104, 104), target.DesiredSize);
             }
 
-            private static TestRoot CreatedRoot(
+            [Fact]
+            public void Measure_Arranges_Child_To_Rounded_BorderThickness()
+            {
+                Canvas child;
+                var target = new Border
+                {
+                    BorderThickness = new Thickness(1),
+                    Width = 82,
+                    Height = 82,
+                    Child = child = new Canvas(),
+                };
+
+                var root = CreateRoot(1.5, target);
+
+                root.LayoutManager.ExecuteInitialLayoutPass();
+
+                // - 1 pixel border thickness is rounded up to 1.3333; for both sides it is 2.6666
+                // - Size of 82 needs no rounding
+                // - Minus border thickness, space for child is 82 - 2.6666 = 79.3333
+                Assert.Equal(1.3333, child.Bounds.Left, 3);
+                Assert.Equal(1.3333, child.Bounds.Top, 3);
+                Assert.Equal(79.3333, child.Bounds.Width, 3);
+                Assert.Equal(79.3333, child.Bounds.Height, 3);
+            }
+
+            [Fact]
+            public void Measure_Arranges_Child_With_Rounded_Margin()
+            {
+                Border child;
+                var target = new Border
+                {
+                    Width = 220,
+                    Height = 220,
+                    Child = child = new Border
+                    {
+                        Margin = new Thickness(0, 25, 25, 25),
+                    },
+                };
+
+                var root = CreateRoot(1.5, target);
+
+                root.LayoutManager.ExecuteInitialLayoutPass();
+
+                // - 25 margin gets rounded up to 25.3333
+                // - Size of 220 needs no rounding
+                Assert.Equal(0, child.Bounds.Left, 3);
+                Assert.Equal(25.3333, child.Bounds.Top, 3);
+                Assert.Equal(194.6666, child.Bounds.Width, 3);
+                Assert.Equal(169.3333, child.Bounds.Height, 3);
+            }
+
+            private static TestRoot CreateRoot(
                 double scaling,
                 Control child,
                 Size? constraint = null)