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The most appropriate unit for measuring liquid volume is the milliliter. This unit is part of the metric system, which is widely used in healthcare settings for its precision and ease of conversion. Milliliters allow for accurate dosage calculations, especially when dealing with medications, which are often prescribed in specific volumes to ensure patient safety and effectiveness.

While teaspoonfuls and ounces may be used in some contexts, they do not offer the same level of specificity and standardization as milliliters. Milligrams, on the other hand, measure mass rather than volume, making them unsuitable for this purpose. Therefore, in the context of measuring liquid volume, milliliters are the optimal choice due to their precision in healthcare applications.