CUPERTINO, Calif. (AP) _ The U.S. semiconductor industry closed out the year with a surge in product orders that were the highest for a single month in over three years, industry officials said.

A trade organization said Wednesday that average monthly bookings, or orders, for the three-month period ending in December were $1.04 billion, a 5 percent increase from the previous month. The December figures represent the highest bookings level since July 1984, when $1.1 billion was recorded.

The industry posted December 1987 billings, or shipments, of $969.3 million, 7 percent higher than the previous month, according to the Semiconductor Industry Association, a trade organization that released the statistics.

But the December billings were 2.7 percent less than the $996.2 million posted in September 1987, the last quarter-ending month, according to the SIA. The December 1987 billings were 25 percent higher than the December 1986 figure.

''The increase in the book-to-bill ratio for December is driven by strong business conditions in end-use markets such as personal computers and engineering workstations,'' said Doug Andrey, SIA's manager of Industry Statistical Programs, in a news release.

Three-month average billings for December were $924.2 million, producing a book-to-bill ratio of 1.13. A book-to-bill ratio of 1.1 means that for every $100 worth of product shipped, or billed, manufacturers got $113 worth of new orders, or bookings.

The Cupertino-based trade organization compiled the statistics from a preliminary survey of key semiconductor manufacturers taking part in the World Semiconductor Trade Statistics program.