WASHINGTON, Oct 12 (Reuters) - U.S. job openings fell in August, but remained significantly high amid labor shortages that are crimping employment growth. Job openings, a measure of labor demand, dropped 659,000 to 10.4 million on the last day of August, the Labor Department said in its monthly Job Openings and Labor Turnover Survey, or JOLTS report, on Tuesday. Hiring decreased 439,000 to 6.3 million. The government reported last Friday that nonfarm payrolls increased by only 194,000, the smallest gain since December 2020, after increasing 366,000 million in August. (Reporting by Lucia Mutikani) Our Standards: The Thomson Reuters Trust Principles.