THE SEVEN AT Tokyo did useful work on the world's system of exchange rates. If they left the details vague, they were clearer on the crucial element. They declared that they share a responsibility to coordinate their economies. This time the United States seems to mean it. The days of the hands-off currency float are over.

The Tokyo summit meeting did not try to decide whether the dollar has now fallen too low or the yen has risen too high. That's a large question, and one on which the seven are not prepared to agree. But they have sensibly committed themselves at least to keep talking about the exchange rates and the reasons for their swings.

Why did the dollar rise so high in the early 1980s? The huge budget deficits in this country were the key to it. They pushed up interest rates, attracting flows of foreign money on a scale that this country had never seen before. That happened, by coincidence, at a time when other countries, most notably Japan, were deregulating their financial systems and permitting capital to move abroad more easily. As foreign investors bought dollars, they bid the price up to levels that put unmanageable burdens on many American manufacturers and exporters.

That experience illustrates the truth that exchange rates are not independent of governments' domestic policies. When they get out of line, the first place to look for the source of the trouble is at home. The Tokyo communique declared that future consultation will not be limited to conventional international issues but will reach beyond them to consider countries' internal growth, their inflation rates and their budget deficits. Those are subjects that several of these governments, including the United States', until recently said were nobody's business but their own.

In the history of the Reagan administration, 1981 to early 1985 will be remembered as the period in which the United States refused to recognize any responsibility for exchange rates, or any international obligations that might conflict with its economic plans. But there was a change at the beginning of 1985. One reason was the appointment of James A. Baker as secretary of the Treasury. Another was the dollar's exchange rate, by then more than 50 percent higher than four years earlier. Since then the United States has been taking a steadily more active part in managing the world's currency system -- very much to the benefit of this country and all others that depend on world trade for their prosperity. The currency system is not a robot. It has to be managed, and only the United States can provide the necessary leadership. At Tokyo, the American resumption of that essential leadership was more explicit and more effective than it has been for many years.