China is rising fast and is expected to eclipse the United States economically in the future - its gross domestic product is tipped to overtake that of America by 2045.
While Mr Bush has only given Mr Hu an hour of his time for a state lunch, the global balance of power is changing and in future meetings, the Chinese will set the timetable.
The rise of China is posing awkward questions for the US, along with the realisation that its days as the world's economic superpower are numbered.
Some analysts see America entering a period of "managed decline" not unlike that which Britain has experienced since the end of the Second World War and the end of empire.
Since the Chinese economy began to open up a quarter of a century ago, there are 400 million fewer desperately poor people in China. Now Beijing wants the remarkable domestic growth story to count for something in global terms. China has already overtaken Britain and France to become the world's fourth largest economy and Mr Hu's visit to Washington represents a culture clash on a global scale. China, the emerging Asian superpower, is ruled with an iron fist by the Communist Party, which has transformed a once centrally planned economy into a free market one, "socialist with Chinese characteristics".
What China repeatedly calls its "peaceful rise" represents a major challenge for the US economy, for its political position and for its role as global policeman.
China, with its endless supply of goods and its thirst for energy, has contributed more to global growth than America in recent years, and Beijing is well aware of this. Mr Hu's visit to America is about boosting China's prestige, earning respect for the world's fastest-growing major economy and matching some of that financial muscle with real political influence.
Japan remains the engine of the Asian economy but it is not registering anything like the double-digit growth rates that China is seeing every year. What makes the rise of China different from Japan's post-war emergence is that China can match its economic growth with a strong army. China is no defeated nation, struggling out of the ashes; instead it is a proud country which likes to remind others of its cultural achievements over thousands of years.
More than half of all industrial goods are made in its factories. The production and export of these goods, their prices kept low by Beijing's manipulation of the renminbi currency, has generated the cash behind China's growing economic power.
Mr Hu was all business at the start of his tour. Dinner at Bill Gates' house in Seattle, followed by a café latte with Howard Schultz, chairman of the Starbucks chain of coffee shops, then on to the Boeing plant, before moving to the east coast, with an itinerary that includes a speech at Mr Bush's alma mater, Yale.
But this opening has been undermined before Mr Hu even arrives. The Chinese leader is being given full military honours on arrival but Mr Hu's journey is not being labelled an official "state visit" as such, but something further down the chain.
Face matters in Asia, and some are reading this as a loss of face for Mr Hu. A dangerous move perhaps, given the shape of things to come. For the Bush administration, the key issue is a huge trade imbalance which is turning ever more political. Cheap Chinese exports are flooding the US market and costing American jobs.
And it is ideological too. China is not a democracy, its attitude on human rights leaves a lot to be desired and the Communist Party's treatment of organised religions angers the devoutly Christian Mr Bush. The feeling in Washington is that Beijing needs to do more to stave off the nuclear threat of North Korea and Iran, while China's courting of oil-rich, but politically suspect, countries in Africa and central Asia also rankles. A mixed bag of complaints, and the perceived absence of a clear line on China has angered some US lawmakers. The Senate Democratic leader, Harry Reid, said that Mr Bush "still has no coherent strategy for managing this nation's relationship with China".
The war in Iraq or Iran's nuclear ambitions are side issues compared with the question about China's "peaceful rise" and what to do when it decides to flex its muscles. Keen to keep the spin positive, senior Chinese foreign affairs officials said Mr Hu's visit would "provide an opportunity for Americans to better understand China's policy of seeking sustainable development and peaceful growth".
The trip will also introduce Mr Hu to the world. He remains a bit of a mystery three years into his leadership and little is known about his personal life, beyond the fact that he is frugal with money, likes ballroom dancing and has a photographic memory. When Mr Bush came to China in November, the two leaders reportedly spoke quite frankly to each other but relations could hardly be described as warm.
In the run-up to Mr Hu's visit, the Chinese released a number of key political prisoners; offered an olive branch to Taiwan, albeit one that Taipei cannot accept; signalled better relations with the Vatican and offered hope that the exiled Tibetan leader, the Dalai Lama, may visit China.
Rise of an eastern superpower
POPULATION
* 1.3 billion
ECONOMICS
* World's fastest growing economy
* Economy has grown 9.5 per cent annually for 25 years
* GDP quadrupled from 1980 to 2000
* 400 million people have been lifted out of poverty in 25 years
TRADE
* 30th largest US trading partner in 1977; now third
* World's second largest recipient of foreign direct investment
* US exports have grown five times faster than to rest of the world. US corporations have invested more than $50bn in China
* Worker earns 5-10 per cent of an American worker's wage
* 2004: Produced half of all digital cameras and 60 per cent of microwaves, photocopiers and DVD players in the world
POLLUTION
* Has 16 of the world's 20 most polluted cities
* Half of the population has polluted water supply
* Produces 3.7 billion tons of sewage a day
* World's largest consumer of coal; second only to US for oil
MILITARY
* 2005: China says it spent $30bn on its military, the Pentagon says $90bn was spent
* 2000: Estimated size is 2.5 million personnel; 10,000 tanks; 400 nuclear warheads
HEALTH
* 2003: UN estimates 840,000 have HIV
* 17 per cent of people live on less than a $1 a day
* One-third of the world's cigarettes are smoked in China
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