WASHINGTON (AP) — Unemployment rates fell in half of U.S. states last month, a sign that September's pickup in hiring was felt around the country.The Labor Department says unemployment rates dropped in 25 states, rose in 14 and stayed the same in 11. That's a modest improvement from August, when unemployment rose in 26 states.Nationwide, employers added 103,000 net jobs in September, nearly double the number created in August. Still, that's not enough to lower the unemployment rate, which stayed at 9.1 percent for the third straight month.Nevada reported the highest unemployment rate for the 16th straight month. It stayed at 13.4 percent for the second consecutive month. California was next. The rate there fell from 12.1 in August to 11.9 percent. Michigan had the third-highest rate, at 11.1 percent.