Tag Archives: expansion

Finding the repetend length of a decimal expansion

Posted on February 8, 2019 by Brent

We’re still trying to find the prefix length and repetend length of the decimal expansion of a fraction , that is, the length of the part before it starts repeating, and the length of the repeating part. In my previous … Continue reading →

Posted in computation, group theory, modular arithmetic, number theory, pattern | Tagged , , , , , , | Comments Off on Finding the repetend length of a decimal expansion

Finding the prefix length of a decimal expansion

Posted on February 2, 2019 by Brent

Remember from my previous post that we’re trying to find the prefix length and repetend length of the decimal expansion of a fraction , that is, the length of the part before it starts repeating, and the length of the … Continue reading →

Posted in number theory, pattern | Tagged , , , , | 3 Comments

Finding prefix and repetend length

Posted on January 29, 2019 by Brent

We interrupt your regularly scheduled primality testing to bring you something else fun I’ve been thinking about. It’s well-known that any rational number has a decimal expansion that either terminates, or is eventually periodic—that is, the digits after the decimal … Continue reading →

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More on repetend lengths

Posted on January 27, 2009 by Brent

In a previous post, I noted that the length of the repetend (repeating portion of the decimal expansion) of a fraction with prime denominator p is at most p-1, and in fact divides p-1. I also said: In fact, there’s … Continue reading →

Posted in group theory, number theory, pattern, primes | Tagged , , , , | 6 Comments

More on decimal expansions

Posted on January 21, 2009 by Brent

Today, I’d like to answer some of the questions I raised in the Decimal Expansion Zoo: Which decimal expansions terminate, and which are repeating—and how does it relate to the denominator? As we know, the decimal expansion of every rational … Continue reading →

Posted in number theory, pattern | Tagged , | 15 Comments

Decimal expansion zoo

Posted on September 23, 2008 by Brent

In a comment on a previous post about rational numbers and decimal expansions, Steve Gilberg noted: I’ve been fascinated at how any multiple of 1/7 that’s not an integer repeats the same digits in decimal expression, only starting at different … Continue reading →

Posted in number theory, pattern | Tagged , , | 14 Comments