Gold and silver prices fell further today as a strong U.S. dollar and anticipation of reduced inflation in the United States continued to drive investors away.

Nonetheless, the decline in precious-metals prices was not as abrupt as on Monday, when gold slipped $14.40 an ounce and silver 69 cents in New York trading. Today gold fell another $3.30 on New York's Commodity Exchange to $432.50, and silver fell 2 1/2 cents to $8.555.

The strog U.S. dollar continued its winning ways, closing slightly higher against most major European currencies.

The strength of the dollar is "the whole answer in a nutshell," according to Bette Raptopoulos, precious-metals analyst at the big brokerage firm Bache Halsey Stuart Shields Inc.

Silver prices, which have fallen faster than gold prices, have been hurt not only by the strong dollar but also by the government's determination to sell silver from its stockpile and by worries that the Hunt brothers of Texas may have to sell some of their 63 million ounces to pay off bank loans (acquired when a plunge in silver prices 15 months go strapped them for cash and almost triggered the demise of several brokerage firms, including Bache).

Today the House approved a bill authorizing the General Services Administration to sell 105.12 million ounces of silver over the next three years.

The world's disaffection with gold and silver is a sharp turnaround from 18 months ago when the crisis in Iran and Afghanistan and an inflationary surge in the United States helped fuel a skyrocketing of precious-metals prices that sent silver about $50 an ounce and gold close to $900.

Today, despite continued problems in Iran and Afghanistan, as well as prolonged political problems in Poland and a new Socialist government in France, investors are shunning precious metals in favor of investing in the United States.

Part of the attractiveness of the United States is its high interest rates. When investors can earn 15 percent of 16 percent interest on high-grade investments, it makes little sense to plunk funds into gold and silver, which yield no return (except when their prices rise) and cost money to store. But even the prospect of lower interest rates here -- caused in part by lessened inflation and in part by a sharp slowdown in the rate of monetary growth that should permit the Federal Reserve Board to ease up on its tight money policies -- has not seemed to impel investors back to the metals markets.

Many smaller investors, not to mention some wealthier ones, may remember the beating they took when gold and silver plummeted from their giddy highs of January 1980 to less than $500 an ounce for gold and $10.80 for silver in late March 1980.

Raptopoulos of Bache said the poor European economies, unrest in Italy, and fears of steps that might be taken by the French Socialists are convincing European investors to put their money in the United States, boosting demand for the dollar.

Some analysts think gold could fall below $300 an ounce under current conditions.