A primer from Chinese premier

''Do you know how many characters there are in Chinese?'' Premier Zhao Ziyang asked an American high school student. ''There are 40,000 to 50,000 in the dictionary,'' he said, answering his own question. ''But I may know less than 3,000,'' he added modestly. ''Sometimes I forget how to write the complicated characters because I don't practice enough.''

So went the conversation during the premier's recent visit with a group of students from Washington, D.C., who just returned from China where thay toured as his personal guests. It was an afternoon of chit-chat, on-the-spot history lessons, and personal encouragement in Chinese studies from the head of China's government.

The June 21 visit began inside the exclusive walled compound of Zhongnanhai, which houses the offices of the Central Committee of the Communist Party and the residences of some of China's top leaders. Few visitors have been allowed inside , and no one could remember when a Chinese leader had taken guests, especially Americans, on a personal tour.

In the brilliantly colored Zi Guang Ge (Pavilion of Purple Light), the premier served the young tourists Chinese pastries and cookies, freshly made ice cream, and chilled litchi fruit flown in specially from Canton. His formal welcoming remarks, made in the glare of television cameras, recalled his visit to the students' Sidwell Friends School during a trip to Washington last January.

''The warmth of friendship you showed the Chinese people left a deep impression on me,'' he said on that snowy morning.

His apparently spontaneous response was to invite all the students enrolled in the Chinese studies program at Sidwell Friends to tour China for three weeks as his official guests. Sidwell's 20 Chinese studies students and seven faculty members and their spouses took him up on the offer.

Premier Zhao's interest in Sidwell and his generous invitation were prompted by the tragic case of John Zeidman, a graduate of the school who lost his life while he was an exchange student in China in late 1981. Zeidman's father, Philip , subsequently established a memorial endowment for a Chinese studies program at the school. The program enrolled its first students last fall.

But the premier also may have had a larger aim in trying to correct the lopsidedness in educational programs linking the United States with China. There are tens of millions of Chinese students studying English in thousands of middle schools (high schools) throughout China, and some primary schools offer English.

On the other hand, there are only a little over 100 secondary schools in the US offering Chinese, according to a study by the Geraldine R. Dodge Foundation. Many of these are schools in US cities where there are large Chinese communities. (In the past two years, 37 new Chinese language studies programs have been set up in secondary schools with help from the Dodge foundation.)

Student exchange programs reflect a similar disparity in numbers. At least 12 ,000 Chinese are studying in the US (mostly in science and technology), while only a few hundred American students are in China (mainly in short-term language programs).

Such imbalance is typical of the educational links between a developed and a developing country, said a US Embassy official here. Nevertheless, both governments are encouraging more interest in Chinese studies.

''We all know that language is the key to friendship,'' Zhao said to the students at his ice-cream party. ''I feel there should be more Chinese young people studying your language and more American young people studying our language.''

He urged them to learn all they could about Chinese literature and history. ''You must teach these students Tang Dynasty poetry!'' he told Dawn Sun, who teaches Chinese at Sidwell Friends.

Later the premier took his guests on a walking tour of Zhongnanhai. He set a fast pace. On the steps of Emperor Kuang Hsu's Yin Tai palace, while members of the tour group caught their breath, he began one of the afternoon's history lessons.

It was 1898, during the twilight years of the Qing Dynasty, he explained. In an attempt to strengthen a decaying, feudal empire against internal rebellion and external aggression, Emperor Kuang Hsu issued many reform edicts that summer.

Conservative officials at Peking's Imperial Court as well as in the provinces felt threatened by the sweeping changes. They convinced the young Emperor's aunt , the powerful Empress Dowager, to quash the movement by certain scholar-officials who wanted to make the government more democratic and to learn from the West.

Finally, Yuan Shih-kai, commander of the army, betrayed the reformers, shifted his support to the empress, and staged a coup. The ''Hundred-Day Reform'' ended and the emperor was placed under house arrest here in his own palace. His key followers fled or were executed.

No one asked what lessons China's current reformers under Deng Xiaoping's leadership may have drawn from the 1898 episode. But Zhao displayed a lively interest in the subject and seemed to want to stimulate others' interest in it as well.

The following night, China's national television network gave the students' first day in Peking eight minutes of coverage during its 30-minute news program. The next night, there was another seven minutes of coverage showing the students visiting their sister school in Peking, where they attended classes, played sports, and joined in a Chinese-American talent show.

The exceptional publicity and VIP treatment accorded the students as they traveled across China amplified the outgoing temperament of China's premier. It set an example for the ''broad masses,'' as the public here is often called, to get to know Westerners.

Beginning in 1985, two students in Sidwell's Chinese program will be brought to China each year for language training and a tour of the country at the expense of the Chinese government.

Clearly China's leaders are taking their own ''open door'' policy to heart. Zhao is especially exuberant in promoting exchanges between young people.

And last year, Communist Party General Secretary Hu Yaobang invited 3,000 Japanese students to tour China as his official guests. They are all scheduled to arrive in September.