diff --git a/packages/flutter/lib/src/widgets/draggable_scrollable_sheet.dart b/packages/flutter/lib/src/widgets/draggable_scrollable_sheet.dart
index 4110266db9..6d0dcc67e9 100644
--- a/packages/flutter/lib/src/widgets/draggable_scrollable_sheet.dart
+++ b/packages/flutter/lib/src/widgets/draggable_scrollable_sheet.dart
@@ -15,6 +15,7 @@ library;
 
 import 'dart:math' as math;
 
+import 'package:collection/collection.dart';
 import 'package:flutter/foundation.dart';
 import 'package:flutter/gestures.dart';
 
@@ -909,14 +910,18 @@ class _DraggableScrollableSheetScrollPosition extends ScrollPositionWithSingleCo
     }
   }
 
-  bool get _isAtSnapSize {
-    return extent.snapSizes.any((double snapSize) {
+  // Checks if the sheet's current size is close to a snap size, returning the
+  // snap size if so; returns null otherwise.
+  double? _getCurrentSnapSize() {
+    return extent.snapSizes.firstWhereOrNull((double snapSize) {
       return (extent.currentSize - snapSize).abs() <=
           extent.pixelsToSize(physics.toleranceFor(this).distance);
     });
   }
 
-  bool get _shouldSnap => extent.snap && extent.hasDragged && !_isAtSnapSize;
+  bool _isAtSnapSize() => _getCurrentSnapSize() != null;
+
+  bool _shouldSnap() => extent.snap && extent.hasDragged && !_isAtSnapSize();
 
   @override
   void dispose() {
@@ -929,7 +934,7 @@ class _DraggableScrollableSheetScrollPosition extends ScrollPositionWithSingleCo
 
   @override
   void goBallistic(double velocity) {
-    if ((velocity == 0.0 && !_shouldSnap) ||
+    if ((velocity == 0.0 && !_shouldSnap()) ||
         (velocity < 0.0 && listShouldScroll) ||
         (velocity > 0.0 && extent.isAtMax)) {
       super.goBallistic(velocity);
@@ -981,6 +986,13 @@ class _DraggableScrollableSheetScrollPosition extends ScrollPositionWithSingleCo
         super.goBallistic(velocity);
         ballisticController.stop();
       } else if (ballisticController.isCompleted) {
+        // Update the extent value after the snap animation completes to
+        // avoid rounding errors that could prevent the sheet from closing when
+        // it reaches minSize.
+        final double? snapSize = _getCurrentSnapSize();
+        if (snapSize != null) {
+          extent.updateSize(snapSize, context.notificationContext!);
+        }
         super.goBallistic(0);
       }
     }
diff --git a/packages/flutter/test/widgets/draggable_scrollable_sheet_test.dart b/packages/flutter/test/widgets/draggable_scrollable_sheet_test.dart
index 4f44965fba..47a2c295fb 100644
--- a/packages/flutter/test/widgets/draggable_scrollable_sheet_test.dart
+++ b/packages/flutter/test/widgets/draggable_scrollable_sheet_test.dart
@@ -1892,4 +1892,30 @@ void main() {
     expect(receivedNotification!.shouldCloseOnMinExtent, isFalse);
     controller.dispose();
   });
+
+  // Regression test for https://github.com/flutter/flutter/issues/140701
+  testWidgets('DraggableScrollableSheet snaps exactly to minChildSize', (
+    WidgetTester tester,
+  ) async {
+    double? lastExtent;
+
+    await tester.pumpWidget(
+      boilerplateWidget(
+        null,
+        snap: true,
+        onDraggableScrollableNotification: (DraggableScrollableNotification notification) {
+          lastExtent = notification.extent;
+          return false;
+        },
+      ),
+    );
+
+    // One of the conditions for reproducing the round-off error.
+    await tester.fling(find.text('Item 1'), const Offset(0, 100), 2000);
+    await tester.pumpFrames(
+      tester.widget(find.byType(Directionality)),
+      const Duration(milliseconds: 500),
+    );
+    expect(lastExtent, .25);
+  });
 }