FINALLY, DISTRICT residents have a fair idea of the size of the financial obligations accumulated by the city in the past. Drawing on studies that took independent financial experts years to complete, Mayor Barry now reports that the figure is about $284 million. About 60 percent of this sum is attributed to debts that the city's federal overseers casually and carelessly allowed to pile up before home rule went into effect. The remaining 40 percent flows from hidden debts unmasked by the changes in accounting procedures made in the process of finding out what the city actually owes. But $284 million is a hefty sum, and it was certainly no fun for Mayor Barry to report what the city owes. It is, nonetheless, bracing after all these years of innocence and ignorance to get the truth, or something reasonably close to it, about the city's tangled financial past.

Before going any further, let us make a crucial distinction. The new figure of accrued or accumulated debt is, so to speak, the apple of the District's financial eye. But there is an orange: the current budbetary deficit, the amount by which expenditures are estimated to exceed revenues in fiscal 1980, which ends on Sept. 30. That figure is at least $90 million and perhaps as high as $172 million -- in any event, a very large figure for one year. Mayor Barry may have responsibilty for only a small part of the debt of $284 million that had accumulated by last Sept. 30. He has full responsibility for most of the $90- to $172-million deficit expected by next Sept. 30.

For the orange -- this year's deficit -- the mayor has already announced a series of measures that, as we observed earlier, are tough and painful but not tough and painful enough. Meanwhile, the mayor has made the changes in annual accounting procedures that will, he insists, end the intolerable situation in which the city was running essentially in the financial blind.

For the apple -- the accumulated debt -- Mayor Barry is taking another approach, one we heartily salute. He has invited the whole community -- the federal government, business, academics, politicians, neighborhood leaders and citizens -- to give him their ideas over the next 60 days on how to formulate a plan for the District's longer-range financial concerns.

Meanwhile, we want to emphasize the particular duty of the Congress. It created much of the past problem of exercising sloppy supervision in the years when it arrogated the exclusive right of supervision to itself. It is creating much of the current problem by arbitrarily determining -- and sometimes even changing, after the fiscal year has begun -- how much it will pay the city in place of taxes. Congress needs to approve the president's proposal to set a standard percentage of the city's budget as the amount of the federal payment to the city. It needs immediately to appropriate the $66 million remaining from the $300 million the Congress had authorized for the District this year. That is a minimum -- and essential -- beginning.