Final answer:
U.S. State Legislatures require a three-fourths majority to ratify an amendment for it to become law. This requirement is clearly stipulated in the procedures for amending the Constitution.
Step-by-step explanation:
When discussing the ratification of amendments to the U.S. Constitution by state legislatures, the required percentage is a three-fourths majority. This is explicitly stated where it says that amendments proposed to the Constitution must be ratified by three fourths of the said Legislatures to be valid as part of the Constitution. Notably, this method of ratification has been used, for example, to repeal Prohibition with the 21st Amendment. For a new amendment to become law, ratifying conventions in three-fourths of the states must approve it.
It's also worth mentioning that the Constitution itself was ratified once it had the approval of at least nine states, as per Article 7 of the proposed U.S. Constitution. This was a lower threshold designed to ensure the Constitution could become effective without unanimous consent from all thirteen original states.