Millions of Americans have been cheating the government out of billions of dollars a year by claiming non-existent children and parents as dependents for tax purposes, the Internal Revenue Service says.

The year after Congress required that children 5 or older have Social Security numbers, the number of dependent exemptions dropped by 7 million below what had been predicted. That brought in an extra $2.8 billion in taxes in 1987 alone, the IRS says.Returns filed by 11,627 couples and individuals showed declines of seven or more dependents claimed from the previous year. Nearly 67,000 claimed four, five or six fewer dependents than before. In most cases, the exaggerated claims had been made for several years.

"The decrease is particularly significant because it seems to indicate that a 20-year trend of increasing numbers of improper dependency exemptions has finally been reversed," concluded IRS researcher John A. Szilagyi.

The study indicated that most of the cheating was being done by single taxpayers and by married people who filed separate returns. The number of dependents claimed by singles dropped 48.3 percent from 1986 to 1987; claims by married people filing separately declined 28 percent; the number claimed by couples filing joint returns dropped 3.9 percent.

There was not nearly so much variance when the tax returns were divided into income groups. Those with income under $25,000 showed a 7 percent decline in dependents claimed; between $25,000 and $50,000, the number fell 4 percent, and those with income over $50,000 reported 4.9 percent fewer dependents than a year before.

Returns filed for 1987 claimed 69.7 million dependents; the IRS had anticipated 76.7 million. These figures do not include the personal exemptions allowed taxpayers and their spouses.