A computer-scanning check-out system used by Giant Foodstores in the Washington area will be complete tomorrow when the last store, at 13344 Laurel-Bowie Rd. in Laurel, converts to the new system.

The change from manual price checking to computer scanning, using a a laser beam to read each item and its price, cost the Landover-based company $25 million over 4 1/2 years.

It is the most significant change in the supermarket industry since the inception of the supermarket itself," said Donald Buchanon, the company's vice president for data processing.

Giant officials say the company is the first retail food chain in the world to convert entirely to the scanning system.

All goods are marked with a code that is read by the scanner, and the price is displayed automatically. The company said studies indicate the system speeds up the average checkout time by 6 percent.

The computerized system also permits customers with identification cards issued by a Giant store to cash personal checks at any of the 117 markets in the chain.

Giant officials said future plans include improving the system to distinguish tax-deductible drug items, and to issue better item descriptions on customer receipts.

When the computer scanning systems were initiated several years ago, some consumer organizations complained they would lead to elimination of clearly marked price tags on items, since the scanner reads a computer imprint unintelligible to customers.

A Giant official said yesterday that although the company still receives some complaints about the system, "the vast majority think it's great."