# Tag Archives: expansion

## More on repetend lengths

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

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

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