diff --git a/examples/demo.rs b/examples/demo.rs
index fb930b3..1c3d155 100644
--- a/examples/demo.rs
+++ b/examples/demo.rs
@@ -6,6 +6,7 @@ use bevy::{
 use big_space::{
     camera::{CameraController, CameraInput},
     propagation::IgnoreFloatingOrigin,
+    reference_frame::RootReferenceFrame,
     world_query::GridTransformReadOnly,
     FloatingOrigin, GridCell,
 };
@@ -21,10 +22,10 @@ fn main() {
         ))
         .insert_resource(ClearColor(Color::BLACK))
         .add_systems(Startup, (setup, ui_setup))
-        .add_systems(Update, (cursor_grab_system, ui_text_system))
+        .add_systems(PreUpdate, cursor_grab_system)
         .add_systems(
             PostUpdate,
-            highlight_nearest_sphere.after(TransformSystem::TransformPropagate),
+            (highlight_nearest_sphere, ui_text_system).after(TransformSystem::TransformPropagate),
         )
         .run()
 }
@@ -98,7 +99,7 @@ fn ui_setup(mut commands: Commands) {
         TextBundle::from_section(
             "",
             TextStyle {
-                font_size: 28.0,
+                font_size: 18.0,
                 color: Color::WHITE,
                 ..default()
             },
@@ -148,9 +149,9 @@ fn highlight_nearest_sphere(
         return;
     };
     // Ignore rotation due to panicking in gizmos, as of bevy 0.13
-    let (scale, _, translation) = transform.to_scale_rotation_translation();
+    let (scale, rotation, translation) = transform.to_scale_rotation_translation();
     gizmos
-        .sphere(translation, Quat::IDENTITY, scale.x * 0.505, Color::RED)
+        .sphere(translation, rotation, scale.x * 0.505, Color::RED)
         .circle_segments(128);
 }
 
@@ -165,6 +166,7 @@ fn ui_text_system(
     origin: Query<GridTransformReadOnly<i128>, With<FloatingOrigin>>,
     camera: Query<&CameraController>,
     objects: Query<&Transform, With<Handle<Mesh>>>,
+    reference_frame: Res<RootReferenceFrame<i128>>,
 ) {
     let origin = origin.single();
     let translation = origin.transform.translation;
@@ -175,10 +177,20 @@ fn ui_text_system(
     );
 
     let translation_text = format!(
-        "Transform: {:>8.2}x, {:>8.2}y, {:>8.2}z",
+        "Transform: {}x, {}y, {}z",
         translation.x, translation.y, translation.z
     );
 
+    let real_position = reference_frame.grid_position_double(origin.cell, origin.transform);
+    let real_position_f64_text = format!(
+        "Combined (f64): {}x, {}y, {}z",
+        real_position.x, real_position.y, real_position.z
+    );
+    let real_position_f32_text = format!(
+        "Combined (f32): {}x, {}y, {}z",
+        real_position.x as f32, real_position.y as f32, real_position.z as f32
+    );
+
     let velocity = camera.single().velocity();
     let speed = velocity.0.length() / time.delta_seconds_f64();
     let camera_text = if speed > 3.0e8 {
@@ -204,8 +216,9 @@ fn ui_text_system(
 
     let mut debug_text = debug_text.single_mut();
 
-    debug_text.0.sections[0].value =
-        format!("{grid_text}\n{translation_text}\n{camera_text}\n{nearest_text}");
+    debug_text.0.sections[0].value = format!(
+        "{grid_text}\n{translation_text}\n\n{real_position_f64_text}\n{real_position_f32_text}\n\n{camera_text}\n{nearest_text}"
+    );
 
     fun_text.single_mut().sections[0].value = fact_text
 }
diff --git a/examples/error_child.rs b/examples/error_child.rs
index a027e53..4737615 100644
--- a/examples/error_child.rs
+++ b/examples/error_child.rs
@@ -17,10 +17,12 @@ fn main() {
         .run()
 }
 
-// The distance being used to test precision. A sphere is placed at this position, and a child is
-// added in the opposite direction. This should sum to zero if we had infinite precision.
-const DISTANT: DVec3 = DVec3::new(1e17, 0.0, 0.0);
-const ORIGIN: DVec3 = DVec3::new(200.0, 0.0, 0.0);
+// The nearby object is 200 meters away from us. The distance object is 100 quadrillion meters away
+// from us, and has a child that is 100 quadrillion meters toward us (relative its parent) minus 200
+// meters. If we had infinite precision, the child of the distant object would be at the same
+// position as the nearby object, only 200 meters away.
+const DISTANT: DVec3 = DVec3::new(1e17, 1e17, 0.0);
+const NEARBY: DVec3 = DVec3::new(200.0, 200.0, 0.0);
 
 fn setup_scene(
     mut commands: Commands,
@@ -34,19 +36,22 @@ fn setup_scene(
         ..default()
     });
 
-    // A red sphere located at the origin
+    // A red sphere located nearby
     commands.spawn((
         PbrBundle {
             mesh: mesh_handle.clone(),
             material: materials.add(Color::RED),
-            transform: Transform::from_translation(ORIGIN.as_vec3()),
+            transform: Transform::from_translation(NEARBY.as_vec3()),
             ..default()
         },
         GridCell::<i128>::default(),
     ));
 
     let parent = root.translation_to_grid(DISTANT);
-    let child = root.translation_to_grid(-DISTANT + ORIGIN);
+    // This function introduces a small amount of error, because it can only work up to double
+    // precision floats. (f64).
+    let child = root.translation_to_grid(-DISTANT + NEARBY);
+
     commands
         .spawn((
             // A sphere very far from the origin
@@ -86,8 +91,8 @@ fn setup_scene(
     // camera
     commands.spawn((
         Camera3dBundle {
-            transform: Transform::from_translation(ORIGIN.as_vec3() + Vec3::new(0.0, 0.0, 8.0))
-                .looking_at(Vec3::ZERO, Vec3::Y),
+            transform: Transform::from_translation(NEARBY.as_vec3() + Vec3::new(0.0, 0.0, 20.0))
+                .looking_at(NEARBY.as_vec3(), Vec3::Y),
             ..default()
         },
         GridCell::<i128>::default(),