Final answer:
In cases of moderate dehydration where oral rehydration fails or vomiting persists, intravenous fluid administration is the next step. This typically involves the use of isotonic saline to replace lost electrolytes and water.
Step-by-step explanation:
If a child with moderate dehydration fails to take the required amount of oral rehydration solution or continues to vomit, intravenous (IV) fluid administration should commence. This is because oral and other non-IV methods may not be effective due to ongoing vomiting or inability to retain fluids. For dehydrated patients, fluids given intravenously usually consist of saline at a concentration that is isotonic with respect to body fluids. This isotonic saline helps to replenish the electrolytes and water the body has lost during dehydration. It is crucial to administer these fluids under medical supervision to ensure the patient's safety and effective treatment.