Tennessee’s unemployment numbers rose sharply to 6.4 percent in May, nearly a full percentage point above the national rate. Governor Bredesen says the unemployment figures underline the importance of the buyouts of around 2,700 state workers as the state prepares for more difficult economic times ahead. The state had 8,500 fewer manufacturing jobs in May compared with the same month last year, while financial jobs were down 2,400. Tennessee also lost 2,700 professional, scientific and technical services jobs between April and May. The state’s unemployment rate last month was 5.4 percent. The national unemployment rate jumped from 5 percent in April to 5.5 percent in May.