Quick, if your stock just reached 38 5/16, what’s the going price, in real money? The answer $38.31 probably didn’t flash right into your head, and no wonder. Only stock junkies think in sixteenths.

By the end of the year, even junkies won’t have to bother. The U.S. stock markets are converting to decimal pricing.

In theory, this change should be profitable for small investors. In practice, however, we’ll have to see. Fractional stock pricing goes back to the Spanish portion of our heritage, when one of the dominant currencies was silver coins cut into eighths for smaller transactions (“pieces of eight”). The U.S. markets priced stocks in eighths until 1997. Then they cut the fraction in half, to sixteenths. The smaller the fractional price, the more competitive markets can be.

As an example, take a $20 stock that’s on the rise. If it’s priced in eighths, the next highest bid has to be 20 1/8 (about $20.13). If it’s priced in sixteenths, however, the next highest bid can be just 20 1/16 ($20.06). In other words, you can buy the stock at a better price.

If you’re selling into a falling market, a smaller fraction means you can also sell at a better price. The smallest amount by which prices normally change is called a “tick.”

The financial industry, with the Securities and Exchange Commission, has been working on decimalization for the past three years. An SEC order early this month set the phase-in date at July 3.

By the end of the year, all stocks and their options will be quoted in dollars and cents.

At the same time, the size of the tick will drop to a nickel. On a rising $20 stock, the next highest bid will be $20.05. A pilot program will test ticks of only a penny. In that case, the next highest bid on a $20 stock would be just $20.01. Penny ticks are expected to be widely available in 2001.

For small investors, I see two advantages.

First, you’ll be able to track stock prices more easily, when you no longer have to translate from fractions into dollars and cents.

Second, small investors should be able to buy and sell at a better price. For example, if you’re bidding for a rising $20 stock, you might buy at $20.05 or less per share. Previously, it would have cost you at least $20.06.

That’s a $10 saving on 1,000 shares. For active traders, it adds up.

Eventually, however, the new system might lead to higher investment fees. That’s because your gain is potentially your brokerage firm’s loss.

The firm’s profit depends, in part, on the “spread” the difference between a stock’s buying and selling price at any given moment.

Currently, a stock you buy at 20 might carry a selling price of 19 15/16. The 6 cents in the middle is split among the various firms that deal with the transaction.

Starting in July, those firms will have only 5 cents to split. Next year, some stock transactions will leave the industry only with a penny.

“We’re going to see an intense period of competition among the firms that create markets for stocks,” says William Freund, director of the Center for the Study of Equity Markets at Pace University in New York.

Smaller ticks will induce much more trading volume, as investors jockey for better buying and selling prices, Don Kittell, executive vice president of the Securities Industry Association in New York, told my associate, Dori Perrucci. More trading volume means more profit.

But in a poor market, when trading column and profits slow, firms will look for other ways to charge. That could lead to higher commissions or fees.

For investors who trade large amounts of stock, including mutual funds, the smaller tick may not be a money-saver, says Kenneth Kavajecz, an assistant professor of finance at the Wharton School in Philadelphia.

With ticks closer together, there are more possible prices for a stock. As a result, fewer shares are offered at each price (or line up to be sold at each available future price).

Institutions will have to break up large orders into smaller ones, to get a particular price especially on stocks that are lightly traded. So their transaction costs may rise.

If trading costs rise at mutual funds, guess who will pay?

Syndicated columnist Jane Bryant Quinn can be reached in care of the Washington Post Writers Group, 1150 15th St., Washington D.C. 20071-9200.