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Tag Archives: decimal
Finding the repetend length of a decimal expansion
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 decimal, expansion, group theory, rational, repeating, repetend, totient
Comments Off on Finding the repetend length of a decimal expansion
Finding the prefix length of a decimal expansion
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
Finding prefix and repetend length
We interrupt your regularly scheduled primality testing to bring you something else fun I’ve been thinking about. It’s wellknown that any rational number has a decimal expansion that either terminates, or is eventually periodic—that is, the digits after the decimal … Continue reading
More fun with infinite decadic numbers
This is the sixth in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does “close to” mean?, The decadic metric, Infinite decadic numbers). Last time I left you … Continue reading
Posted in arithmetic, infinity, number theory
Tagged decadic, decimal, fractions, integers, representation
4 Comments
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 p1, and in fact divides p1. I also said: In fact, there’s … Continue reading
Posted in group theory, number theory, pattern, primes
Tagged decimal, expansion, fractions, length, repetend
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
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
Rational numbers and decimal expansions
As you may remember from school, rational numbers have a terminating or eventually repeating (periodic) decimal expansion, whereas irrational numbers don’t. So, for example, 0.123123123123…, with 123 repeating forever, is rational (in fact, it is equal to 41/333), whereas something … Continue reading