diff --git a/core/lib/Drupal/Core/Config/Config.php b/core/lib/Drupal/Core/Config/Config.php
index c9084b7..18afe28 100644
--- a/core/lib/Drupal/Core/Config/Config.php
+++ b/core/lib/Drupal/Core/Config/Config.php
@@ -426,7 +426,7 @@ public function save() {
     // conform to the schema.
     if ($this->getTypedConfigManager()->hasConfigSchema($this->name)) {
       // Ensure that the schema wrapper has the latest data.
-      $this->setSchemaWrapper();
+      $this->schemaWrapper = NULL;
       foreach ($this->data as $key => $value) {
         $this->data[$key] = $this->castValue($key, $value);
       }
@@ -498,29 +498,22 @@ public function merge(array $data_to_merge) {
   /**
    * Gets the schema wrapper for the whole configuration object.
    *
+   * The schema wrapper is dependent on the configuration name and the whole
+   * data structure, so if the name or the data changes in any way, the wrapper
+   * should be reset.
+   *
    * @return \Drupal\Core\Config\Schema\Element
    */
   protected function getSchemaWrapper() {
-    if (empty($this->schemaWrapper)) {
-      $this->setSchemaWrapper();
+    if (!isset($this->schemaWrapper)) {
+      $typed_config_manager = $this->getTypedConfigManager();
+      $definition = $typed_config_manager->getDefinition($this->name);
+      $this->schemaWrapper = $typed_config_manager->create($definition, $this->data);
     }
     return $this->schemaWrapper;
   }
 
   /**
-   * Sets the schema wrapper property using the current configuration data.
-   *
-   * @return \Drupal\Core\Config\Config
-   *   The configuration object.
-   */
-  protected function setSchemaWrapper() {
-    $typed_config_manager = $this->getTypedConfigManager();
-    $definition = $typed_config_manager->getDefinition($this->name);
-    $this->schemaWrapper = $typed_config_manager->create($definition, $this->data);
-    return $this;
-  }
-
-  /**
    * Gets the definition for the configuration key.
    *
    * @param string $key
@@ -582,6 +575,9 @@ protected function castValue($key, $value) {
         case 'Drupal\Core\TypedData\Plugin\DataType\Boolean':
           $value = (bool) $value;
           break;
+        case 'Drupal\Core\TypedData\Plugin\DataType\Float':
+          $value = (float) $value;
+          break;
         default:
           // Don't change the value.
           break;
@@ -610,7 +606,7 @@ protected function castValue($key, $value) {
    * @return \Drupal\Core\Config\TypedConfigManager
    */
   protected function getTypedConfigManager() {
-    if (empty($this->typedConfigManager)) {
+    if (!isset($this->typedConfigManager)) {
       $this->typedConfigManager = \Drupal::service('config.typed');
     }
     return $this->typedConfigManager;
diff --git a/core/lib/Drupal/Core/Config/Schema/Mapping.php b/core/lib/Drupal/Core/Config/Schema/Mapping.php
index 72de972..92e9a90 100644
--- a/core/lib/Drupal/Core/Config/Schema/Mapping.php
+++ b/core/lib/Drupal/Core/Config/Schema/Mapping.php
@@ -27,7 +27,7 @@ class Mapping extends ArrayElement implements ComplexDataInterface {
   protected function parse() {
     $elements = array();
     foreach ($this->definition['mapping'] as $key => $definition) {
-      if (array_key_exists($key, $this->value)) {
+      if (isset($this->value[$key]) || array_key_exists($key, $this->value)) {
         $elements[$key] = $this->parseElement($key, $this->value[$key], $definition);
       }
     }
diff --git a/core/modules/config/lib/Drupal/config/Tests/ConfigSchemaTest.php b/core/modules/config/lib/Drupal/config/Tests/ConfigSchemaTest.php
index a2b7db1..9f465d7 100644
--- a/core/modules/config/lib/Drupal/config/Tests/ConfigSchemaTest.php
+++ b/core/modules/config/lib/Drupal/config/Tests/ConfigSchemaTest.php
@@ -259,6 +259,7 @@ public function testConfigSaveWithSchema () {
       'array' => array(
         'string' => 1
       ),
+      'float' => '3.14',
       // Not in schema and therefore should be left untouched.
       'not_present_in_schema' => TRUE,
     );
@@ -271,6 +272,7 @@ public function testConfigSaveWithSchema () {
       'array' => array(
         'string' => '1'
       ),
+      'float' => 3.14,
       'not_present_in_schema' => TRUE,
     );
 
diff --git a/core/modules/config/tests/config_test/config/schema/config_test.schema.yml b/core/modules/config/tests/config_test/config/schema/config_test.schema.yml
index faba694..d9851c3 100644
--- a/core/modules/config/tests/config_test/config/schema/config_test.schema.yml
+++ b/core/modules/config/tests/config_test/config/schema/config_test.schema.yml
@@ -98,6 +98,8 @@ config_test.schema_data_types:
   mapping:
     integer:
       type: integer
+    float:
+      type: float
     string:
       type: string
     boolean: