In a development that will mean more inflation ahead, productivity of U.S. business fell more rapidly in the second quarter of this year than at any other time since the government began keeping records in 1947.

The Labor Department reported yesterday that output for each hour worked in nonfarm business dropped 5.7 percent, compared with a drop of 3 percent in the first quarter.

With the economy moving into a recession, a decline in productivity is not surprising: Businesses reduce production before laying off workers. But the sharpenss of the second quarter drop surprised may economists.

On explanation is that while businesses reduced production, they actually continued to hire new workers, a signal that the current economic slump may not boost the unemployment rate as much as previous recessions did.

But the drop is productivity is bound to be inflationary, because while workers were producing less, they were earning more. The combination pushed up the unit labor cost of producing goods by 14.3 percent in the second quarter.

Economists have found that charges in units labor costs usually closely match inflation rates. Over the past year, for instance, unit labor costs went up 10.5 percent while consumer prices rose 10.9 percent, the Labor Department said yesterday.

Courtenay Slator, chief economist at the Commerce Department, said the drop in productivity is "what typically happens at the beginning of a downturn. Output is cut back first and then the cutback in employment comes later."

But in the second quarter, businesses kept adding to payrolls, pushing employment up 1.6 percent. Total hours worked were up only 0.4 percent, however, because the length of the average workweek declined by 1.2 percent.

Nevertheless, the continued hiring during a peroid of failing production may be increase unemployment as much as usual, but also will do little to ease inflation.

Productivity gains have been slowing in recent years, puzzling both government and private economists, who have been at a loss to explain it to their own satisfaction.

Ironically, at the same time the Labor Department was reporting the record productivity decline in the second quarter, it said that the rate of productivity increases over the last two years has not slowed quite as much as was reported earlier.

It revised upward from 1.3 percent to 1.8 percent the increase for nonfarm businesses for 1977, and from 0.5 percent to 1.1 percent the gain in 1978. Unit labor costs rose 6.3 percent in 1977 and 8.1 percent in 1978.

By comparison, productivity grew 3.5 percent in 1976, when the economy was still recovering from the 1974-75 recession. That year unit labor costs went up only 4.7 percent.

The manufacturing sector of the economy fared better in the second quarter than did other areas. Manufacturing productivity rose at a 3.3 percent rate, which means that for nonfarm, nonmanufacturing businesses, productivity plummeted.

The rate of increase in unit labor cost rose to 14.3 percent during the quarter for nonfarm businesses, but worker compensation went up more slowly than it did in the first quarter. In the first three months of the year, higher Social Security tax payments and a higher minimum wage added to the increase.

However, the increase in compensation in the second quarter, at 7.8 percent, was the smallest since the fourth quarter of 1977. Some analysts suggested that the administration's voluntary wage standard, coupled with the first effects of the recession, probably were working together to limit wage increases somewhat.

Meanwhile, the F.W. Dodge Division of Mcgraw-Hill reported that the value of new construction contracts signen in June rose $15.3 billion, 5 percent higher than a year earlier.

Substantial gains in nonresidential building just offset continued weaknesses in home building. George Christie, Dodge's chief economist, said this indicates "that the construction cycle is sliding away from its peak."

The value of nonresidential building contracts in June was 22 percent her than last year, with $4.8 billion worth of contracts signed, mostly for office and manufacturing buildings.

Contracts for residential building posted an 8 percent decline from a year earlier, falling to $7.3 billion -- the report said.