At about 10:51 last Tuesday morning, a young man entered the Washington Federal Savings and Loan Association at 1901 L St. NW and asked an employe whether he could open an account.

He then handed her a bag with a note written on it, demanding money.

In that way, for the 90th time in 1978, a Washington financial institution was robbed.

In several respects, this robbery was typical of the other 89 that occurred earlier in the year.

The robber was a young man. He displayed no weapon. No shots were fired. He apparently acted alone. And police were able to get enough information to make a tentative identification and issue a warrant for the arrest of a suspect. Shorty before the robbery, the robber was seen by a woman in an office building two blocks from the bank. The woman saw the man again shortly after the robbery, according to police, and told them about it when they questioned her later. Police searched the building and found the clothes he had worn to rob the bank with identifying material in them, police said.

Although the 90 robberies that have occurred already this year are far from being a record -- Washington had 115 bank holdups in 1974 -- the number represents a significant increase over the 56 robberies in the city in 1977.

Nationally, according to the FBI, 1978 saw 5,326 such crimes -- including burglaries, robberies and theft of property from banks -- eclipsing the previous record of 5,050 set in 1975. Almost $28 million was obtained in these crimes.

Localy, according to the police, two men, each of whom committed nine or 10 robberies, accounted for almost one-fourth of the robberies.

"A lot has to do with the individuals who are let out of the court system," said an FBI agent, who mentioned the name of one accused bank robber. "You arrest him, he's out that afternoon and he robs another bank. As long as he's out, you know he's going to rob a bank."

Some law enforcement officials ofered no explanation for the substantial increase in robberies this year over last. Others speculated that unemployment, inflation and drugs were responsible for the increase. According to the FBI, 37 percent of those arrested for bank-related crimes are drug users.

Many of the holdups in the District last year were classified by the police as "robbery-fear" rather than armed robbery because no weapon was shown during the holdup. As a result, not a single shot was fired during any of the robberies in Washington in 1978, although an off-duty security guard fired one shot at a fleeing robber after he left the bank.

The amount obtained in a robbery here fluctuated greatly -- from a little as $100 to as much as $8,000. Banks now keep as little money as possible in the cashiers' cash drawers to minimize losses in case of robberies.

In addition, banks are required by federal law to take certain security precautions, including maintenance of an alarm system that goes directly to the nearest law enforcement office, use of "bait money" -- money that has had the serial numbers recorded for tracing after a robbery -- and other devices. Although not required, surveillance cameras, which can be manually or automatically activated, are used in all District financial institutions.

Charles T. (Tony) Booth, who is in charge of the bank robbery squad in the Washington field office of the FBI, said the surveillance cameras are "one of the best instruments for identifying subjects... (It's ) a tremendous asset to have cameras as far as we're concerned."

The average age of the Washington bank robber appears to be going up, according to District police. From 1968 to about 1975, bank robbers were 16 to 20 years old. In the last few years, according to the police, the age has gone to 18 to 21.

At the same time, women have begun showing up as bank robbers. This year seven banks were held up by women, actiing either alone or with a man. Three of the women carried guns.

"Women are becoming more aggressive," said police Capt. Fred Thomas. "You find women doing things they never did before. It's the same with robbers."

Perhaps one reason that bank robberies in Washington have been relatively nonviolent is that bank tellers are insturcted to cooperate with a robber, even though most bank now have bullet-proof glass or extra thick plastic. At the same time, banks are supplied with forms that witnesses are instructed to fill out immediately afterward, describing the robber. Tellers are also told during a day-long course of instruction by District police how to preserve evidence -- for example, not destroying fingerprints.

This year, according to District police, 80 of the 90 robberies already have been closed by the arrest or identification of one or more of the persons accused of having robbed a bank. Maurice J. Cullinane, former District chief of police, who now is executive director of the D.C. Bankers Association, said the "closing rate" for robberies in Washington is high. "If we keep it high," Cullinane said, "I'm sure the rate will drop down again."