WASHINGTON — Nonfarm payrolls increased 431,000 in May, less than economists estimated but the strongest monthly gain in more than 10 years, although private payrolls increased by just 41,000, the Labor Department reported Friday. The unemployment rate fell to 9.7%.

Workers hired for the 2010 Census accounted for more than 95% of the nonfarm payroll gain, bringing the total temporary census staffing to 564,000. May’s nonfarm payroll increase was the largest since March 2000.

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