It is the number that lurks behind much of modern economic life, a figure that helps shape the fortunes of nations and the price of nearly everything. The number hovers around 6.827. It is the nearly fixed rate of exchange between China's currency, the renminbi, and the U.S. dollar. And members of Congress say it is proof that Beijing manipulates its currency to keep its exports cheap -- at the expense of American exports and jobs. They want the government to label China a 'currency manipulator,' which would allow Washington to retaliate against China economically. But the announcement by Chinese authorities on Thursday that President Hu Jintao will be visiting Washington in two weeks is being seen as the beginning of a possible easing of the friction over the renminbi. China experts said it was unlikely that China would have agreed to the visit unless there was at least an informal assurance by the Treasury Department that it would not be named a currency manipulator either on or around April 15 -- the deadline for the Obama administration to submit one of its twice-a-year reports on foreign exchange to Congress. At the same time, economists say the visit and other Chinese moves, suggest China is finally willing to let the renminbi increase in value. Analysts at HSBC, the Hong Kong-based global bank, declared that 'the latest development should make it more likely for Beijing to start moving away from the renminbi's current de facto peg within the next few months, if not weeks.' Before the disclosure of Hu's trip, Goldman Sachs said that China seemed increasingly likely to allow the renminbi to begin a modest appreciation in the next three months. Helen Qiao, the China economist for Goldman Sachs, and others who have spoken with officials in Beijing said that the currency issue appeared to be under active discussion there. But what should be the value of the renminbi? Most Western economists agree that the currency is undervalued, meaning that it would be stronger if it were allowed to float freely in relation to other currencies. But that is about all on which the economists agree. Some argue that the currency is undervalued by an astonishing 50 percent or more. Others contend it is about where it should be, economically speaking, saying the currency is undervalued by about 10 percent. Still others say the renminbi might be overvalued because Beijing does not allow its people to trade it freely for other currencies. If that policy were changed, Chinese savers might move money from low-interest-rate domestic accounts into foreign markets, helping drive down the value of the renminbi. 'Every estimate of the appropriate level of the currency is fraught with uncertainty,' said Eswar S. Prasad, an economist at Cornell University and the former head of the China desk at the International Monetary Fund. 'And it's almost always the case that two methods are going to give you different answers.' Much is at stake, both for China and the United States. If Beijing bowed to American demands and let its currency appreciate by, say, 10 percent, the resulting squeeze on exports would shave about 0.86 of a percentage point off China's annual growth rate, according to a paper by Dani Rodrik, a professor of international political economy at the Harvard Kennedy School of Government. A 25 percent increase in the value of the renminbi would trim Chinese growth by 2.15 percentage points. Before the onset of the global economic crisis, Beijing had been allowing the renminbi to appreciate. From 2005 to 2008, the government let the currency rise by about a fifth against the dollar. It is around the dollar-renminbi rate that the economic might of the United States and a rising China converge and, at times, collide. Many economists say it helps explain the gaping trade deficit of the United States with China. The value of the renminbi in relation to the dollar and other currencies influences, to a greater or lesser degree, the price of everything from a pair of Gap jeans to an Apple iPod. Studies of the renminbi usually reflect one of three schools of economic thought about exchange rates. The first is based on trade and financial transfers, known as current-account deficits, of a country or a group of countries. The second is based on worker productivity. And the third is based on the theory of purchasing power parity, which equalizes the purchasing power of different currencies for a given basket of goods. Researchers from the Washington-based Peterson Institute for International Economics have created a model based on equilibrium exchange rates. Because China sells so many goods in the United States, it runs a giant current-account surplus. It buys dollars to hold down the value of its currency, and has amassed $2.4 trillion in foreign exchange reserves. China is running a current-account surplus equal to about 10.5 percent of its annual economic output. But the Peterson Institute scholars estimate that gap should ideally be 4.2 percent. Based on that assumption, they estimate that the renminbi is about 20 percent undervalued against all currencies, and 40 percent against the dollar. 'It's a level of intervention in foreign exchange markets we have never seen from any country in history,' said Nicholas R. Lardy, a senior fellow at the Peterson Institute. Other economists have come to similar conclusions using a different approach -- productivity. From 1998 to 2008, the total cost of labor that goes into producing one unit of output fell 40 percent in China as workers became better at making goods. Had Beijing not intervened in foreign exchange markets, the higher level of output should have led to higher real wages in dollar terms for the Chinese workers as they approached American levels of productivity. But the currency appreciated just 15 percent in those 10 years. 'The Chinese government is taxing their own workers,' said Moritz Schularick, a professor at Freie Universitat Berlin. Another group of scholars believes the concerns about the renminbi have been overplayed. They cite purchasing power parity, a concept often used to compare prices between developed and developing countries. Such models are often used to adjust for the fact that haircuts, meals at McDonald's and other items cost less in poor countries than in rich nations. One variation of that model, used by Helmut Reisen, suggested that the renminbi was undervalued by only 12 percent in 2008. He acknowledges that it's probably more undervalued now, but not much more. Reisen heads research for the development center of the Organization for Economic Cooperation and Development, based in Paris; his comments do not represent the official view of the OECD. While he says he is not convinced that China needs a major currency revaluation, Reisen agrees with many on the other side of the debate that Beijing needs to overhaul many of its economic policies. The country, he said, needs to replace its emphasis on exports and investment with a focus on increasing spending by Chinese consumers. 'As long as there is high growth, they can allow the currency to appreciate,' he said. 'But I would certainly not urge a 20 percent appreciation.' Prasad of Cornell said one of the most compelling reasons for China to change its currency policy is that it limits Beijing's ability to manage its economy. To maintain the renminbi rate, for instance, the country keeps interest rates very low, which hampers its ability to fight inflation. 'What kind of constraint is the currency policy putting on its ability to balance its growth? That's ultimately what everybody cares about,' he said. 'That's what the Chinese care about, and that's what the U.S. should care about.' 