D.C. school officials, after a year of confusion over one of the city's most vital statistics, have concluded that 80,694 students are enrolled and that the steep decline in classroom population may have ended recently.

The school system's new figure, which was obtained by a head count conducted in October, is slightly lower than the total of 81,300 students officials reported last spring.

That number, which school officials were forced to announce after submitting a budget based on 88,000 students, led to months of battle with the D.C. Council that cost schools about $50 million in budget requests. The confusion over the enrollment count was one reason the school board cited in its 8 to 3 vote to fire Superintendent Andrew E. Jenkins last month.

Fearing enrollment had dwindled even more this fall, school officials spent the last six weeks verifying the October count. And instead of using data collected by computer, they counted by hand. The annual count helps determine the size of the school budget, which now exceeds $520 million.

"This is the kind of news that makes you wipe your brow," said school board member Bob Boyd (Ward 6). "The figures look all right. We're glad it didn't drop beneath 80,000. That would have been very troubling."

Board members said yesterday that continuing losses of students in elementary and junior high grades were balanced by the school system's rapidly expanding preschool classes. Enrollment in preschool programs quadrupled this fall.

The latest tally also suggests that for the first time in five years enrollment in the city's 175 schools may be stabilizing.

For most of the last decade, school system leaders built their budgets around an enrollment count they said was steady at about 88,000 students, but that claim was proved false this year.

Last spring, it was revealed that during the last five years the school system had lost an average of 2,000 students a year -- a steep drop that was not accompanied by any cuts in the system's 11,000-member work force. Officials now say they have several hundred more junior and senior high school teachers than they need.

"Our enrollment problems have really weakened our credibility," school board member Wilma R. Harvey (Ward 1) said yesterday. "We're educators. We're supposed to know how to count. I hope we've put this sad scenario behind us now."

Before his dismissal, Jenkins argued that school board members were "shooting the messenger" because he had discovered the enrollment decline and worked to improve the system's counting methods.

But the board, which credited Jenkins for finding inflated numbers, said his administration waited too long to announce the accurate count, then offered no explanation as to why the decline happened.

An auditing firm hired by the school system last summer also reported that enrollment records often were incomplete or had been destroyed.

The enrollment drop has intensified public pressure on school officials to trim their bureaucracy, but they have yet to take any action. A report just completed by a civic commission that examined the District's budget problems concluded that 800 administrative jobs in the school system should be eliminated.

Nevertheless, Jenkins had proposed a $635 million budget for the next school year, calling for the hiring of nearly 300 more employees.

Board members said yesterday that the new enrollment count is further evidence that Jenkins's budget proposal should be cut substantially before it is sent to the D.C. Council later this month.