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Earlier this week, Securities and Exchange Commission Chairman William Donaldson suggested on CNBC that he would review decimalization. Not the Dewey decimal system, and not the whole edifice of modern mathematics, but the change over the last few years whereby stocks began trading in decimals rather than fractions.

The morning after Donaldson's interview, I posted a comment here on RealMoney on the subject. It became clear from emails that opinions on decimalization are only slightly less divided (and heated) than they are about the current Bush tax cuts. I decided to revisit the subject in longer form.

How did math become such a hot-button topic? It has do with market participants (and some regulators, ahem) fusing stock pricing with minimum stock price differences.

Where It Began

Some brief history first. Until its recent switch to decimals, the U.S. markets stood alone in quoting stock prices in anything but decimals. Why the infatuation with fractions? You can trace its roots back to the Buttonwood Agreement in 1792 that helped create a formal U.S. market for stocks. In trying to set up domestic markets, brokers at the time looked for another market on which to base their own.

For a number of reasons, not least of which was that the U.S. dollar's value was loosely based on the value of the Spanish real, early traders decided to base U.S. markets on the Spanish one. The real had eight parts.

Why eight parts? It had to do with a then-current method of counting on the hands, one that used the thumbs to carry the total you had worked out on your eight fingers. That system led naturally to dividing stock prices into eighths, thus making the smallest possible price change one-eighth, or 12.5 cents.

Pressure began mounting, however, in the latter part of the last century. First, in 1975, commissions were deregulated, so trading costs began coming down. Having obtained a taste of lower trading costs, many investors (and regulators) began looking for other ways to reduce costs for market participants. That 12.5-cent spread started to seem awfully juicy.

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