ARE FRAUDS REALLY costing the government - which means the taxpayers - $25 billion per year? The comptroller general, Elmer B. Staats, suggested as much in Senate testimony last week. But don't put much weight on that figure. It comes from combining one fact - federal aid programs add up to around $250 billion per year - with a Justice Department estimate that fraud may consume from 1 percent to 10 percent of any program's funds. Simple multiplication produces estimated losses anywhere between $2.5 billion and $25 billion. That mainly reinforces Mr. Staat's conclusion that "no one knows" how much federal money id drained away by thefts, false claims for benefits and services, collusion between officials and contractors, and other crimes.

What does bear repeating is Mr. Staat's central point: that the range and intricacy of federal programs provide vast opportunities for abuse; that where officials have systematically looked for fraud, they have tended to find it, and that most agencies do not look hard enough. In saying that, the chief auditor was not charging that most federal bureaus are as scandal-ridden as the General Services Administration seems to be. He simply meant that, until corruption surfaces, administrators tend to concentrate on other things - providing services, getting out grants and maintaining good relations with their clients and Congress.

A lot of expensive bears this out. The student-loan program is one example of a praiseworthy effort that has been savagely abused. Or just recall the multi-billion-dollar housing scandals of several years ago. In its rush to get new inner-city subsidy programs under way, the Department of Housing and Urban Development failed to anticipate how the government and the poor could be bilked by unscrupulous developers, lenders, appraisers and others.

HUD has learned better. A new General Accounting Office survey praises that department as one of the first to have created independent investigative teams whose sole jobs is ferreting out possible fraud. Progress is also being made at the Department of Health, Education and Welfare, where the Office of Inspector General - set up by law last year - is cracking down on abusers of student loans, welfare and medical aid. That office also produced the oft-quoted estimate that "fraud, abuse and waste" in HEW programs cost the taxpayers from $5.5 billion to $6.5 billion last year. As secretary Joseph Califano keeps pointing out, however, over half of that involves wasteful health-care outlays that only Congress can stop.

All this should encourage the Senate to approve the House-passed bill to establish inspectors-general in 12 civilian agencies, including GSA. Beyond that, Congress ought to review every agency's auditing and investigative resources - and, we suspect, enlarge them all. Thct, enlarge them all. The Justice Department, in particular, is badly strapped; its new GSA task force has only a handful of attorneys, barely enough to make a dent. And we have a special charge for the conferees on the civil-service bill: They should make sure that the new law enables agency heads to discipline or fire, more speedily, anyone who engages in or condones wrongdoing or fails to run a program prudently.

But even these tools will not be enough. The most essential element is one that laws and regulations can't secure. That is real commitment to running a tight and proper operation - a commitment that has to start at the top, permeate each agency and be maintained by Congress as well. Firm handling of conspicuous corruption is one part of this. But just as important will be changing a lot of little habits of accommodating friends, winking at small excesses and spending public money as if it were free. If this sounds like post-proposition 13 talk, so be it. We note only that extravagant, undisciplined government was one catalyst for the "taxpayers' revolt" - and that if real improvements are not made soon, the next round of voter reaction may be even more sweeping and convulsive.