It's probably more an English problem than a math problem, but on this page it states

"As a matter of fact, every fraction that has an exact decimal equivalent consists only of powers of 1/2, or the product of 1/5 times a power of 1/2 or some multiple of these fractions (such as 3 times 1/4 = 3/4 = 0.75); there is no other way for an exact decimal equivalent to exist."

The key line is "product of 1/5 times a power of 1/2" which should have instead stated "a power of 1/5 times a power of 1/2". Consider 1/25 = 0.04.

An important detail, considering that it's the main point of the web page.

You missed my favorite: 80/81

Ben Vollmayr-Lee points out that the prime factors of ten, namely 2 and 5, matter when you consider the "does it repeat or terminate?" question. In another base, you'd get a different set of non-repeaters.

In binary fractions, for instance, even tenths are repeating. 1/10decimal = 0.0[0011]binary (hoping I did it right.) This is a peril for the novice accounting programmer, who soon learns that pennies keep disappearing if (s)he represents amounts in units of dollars.

It's fairly easy to generate any repeating decimal you want-- for example,

0.345345345345... = 345/999

Homework problem: find the general formula.

Matt, you're giving away the store. Call 0.345_345_ instead 115/333.

-Brian

Charles:

It's my favorite too—Pat Metheny, Dewey Redman, Michael Brecker, Jack DeJohnette, and Charlie Haden!