Domestic automakers started 1983 with their eighth consecutive 10-day sales gain, a roll that industry officials hope is the beginning of recovery in the U.S. auto market.

The automakers said they sold 112,322 new cars in the first 10 days of January, an 11.6 percent increase over 100,062 sold in January 1982.

The latest figures yield an annual selling rate of 6.8 million cars, marking the eighth time since mid-October 1982 that the domestic industry improved its 10-day sales records over year-ago periods.

Industry analysts credited relatively low new-car financing rates for the continued sales gains. But dealers and their representatives believe they see the beginning of a trend where customers are shopping for products as much as prices.

That dealer optimism is evident in the Washington area, where an estimated 250,000 people paid from $2 to $4 each to attend a 5-day auto show at the D.C. Convention Center last week.

Gerard N. Murphy, managing director of the Automotive Trade Association-National Capital Area, said the attendance exceeded the expectations of dealers, many of whom "were surprised that a lot of people came to buy as much as to look.

The three largest U.S. automakers--General Motors Corp., Ford Motor Co. and Chrysler Corp.--are selling new cars at an 11.9 percent financing rate.

Chrysler said it sold 12,790 cars in the first 10 days this year, a 13.1 percent drop from 14,725 sold in 1982.

GM sold 72,849 cars in early January, up 9.9 percent from 66,281 last year; Ford sold 22,709, up 33.3 percent from 17,033 sold in early January 1982. American Motors Corp., still paced by sales of its Alliance car, registered a 99.6 percent gain with 3,000 cars sold in early January, up from 1,503 sold last year.

Volkswagen of America Inc. sold 974 cars in the period, an 8.1 percent drop from a year ago.

In another development yesterday, Chrysler announced a tentative agreement with a group of creditors on a new plan to finance the company's nearly $2 billion debt.

The creditors agreed to accept shares of Chrysler common stock in exchange for $1.1 billion in Chrysler preferred stock.