Businesses and other employers added jobs in 41 states in October, the best showing in five months, the Labor Department said Tuesday.

The figures indicate the job market is picking up a bit in most parts of the country. Even the nation’s hardest hit states –  Nevada and Michigan — showed declines in their unemployment rates.

The Labor Department said the jobless rate fell last month in 19 states, remained the same in 17 and rose in 14. Unemployment can rise when jobs are created if more people begin searching for work.

The job gains are an improvement from September, when only 16 states reported gains and 34 reported drops. But the additional hiring isn’t large enough to rapidly bring down unemployment in many states.

“These numbers suggest we’ve stabilized and started to show real improvement,” said Anthony Chan, chief economist at JPMorgan Private Wealth Management. “But we’re a long way from crafting the ‘Mission Accomplished’ sign.”

The nation’s four worst-hit states all reported some positive developments, evidence that the economic downturn is loosening.

Nevada reported the first decline in its jobless rate in nearly five years. The state’s unemployment rate, the nation’s highest, fell to 14.2 percent from 14.4 percent in September.

Michigan, with the nation’s second-highest rate, said unemployment declined to 12.8 percent from 13 percent. That’s the first drop below 13 percent in 19 months.

The states with the third- and fourth-highest unemployment rates, California and Florida, also reported job gains.

California added nearly 39,000 jobs in October — the largest net gain in 4 1/2  years. Still, its unemployment rate remained at 12.4 percent, as more people looked for work last month.

Florida’s jobless rate was flat, at 11.9 percent, even after employers added 6,900 jobs last month. In the last year, the state has gained 35,700 jobs, its strongest 12-month gain since May 2007, the state government said.

People who are not actively job hunting are not counted in the unemployment rate. They can range from those who don’t want jobs, to those who are in school or have given up looking.

Nevada, California and Florida were hammered by large housing busts. Michigan suffered as U.S. auto sales plummeted and GM and Chrysler laid off thousands of workers and sought bankruptcy protection.

Recently, Las Vegas has seen a rise in visitors, said Steve Cochrane, a regional economist at Moody’s Analytics. That’s an important boost to Nevada’s tourism and gaming industries. Still, arrivals through the Las Vegas airport are down, which means many visitors are driving in from nearby places. Those visitors tend to spend less at casinos than overseas visitors, Cochrane said.

The latest report also shows how much states such as Nevada are still struggling. The state still saw a decline in total jobs last month. Its unemployment rate fell because many of those out of work are giving up on their job hunts.

Nationwide, employers added 151,000 jobs in October, while the unemployment rate was unchanged at 9.6 percent. Companies added the largest net gain in jobs in six months.