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DENVER—Colorado’s unemployment rate continues to slowly decline.

The state labor department said Tuesday that the unemployment rate declined by one-tenth of a percentage point to 7.8 percent in January.

During January the state gained a total of 19,500 jobs. The private sector added 22,500 jobs in January but government cut 3,000 positions. The biggest gains were in construction, professional and business services and leisure and hospitality.

The state’s survey of households found that the number of people actively looking for work dropped by 3,900 people.

The national unemployment rate for January was 8.3 percent.

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