Tag Archives: rational

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 →

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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 →

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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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The wizard’s rational puzzle (solutions, part 2)

Posted on November 9, 2018 by Brent

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading →

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The wizard’s rational puzzle (solutions, part 1)

Posted on October 24, 2018 by Brent

About two and a half months ago I posted a challenge involving a sadistic math wizard, metal cubes containing rational numbers, and a room full of strange machines. I’ve been remiss in following up with some solutions. (Go read the … Continue reading →

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The wizard’s rational puzzle (mind your p’s and q’s!)

Posted on August 7, 2018 by Brent

You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozy-looking room, with a hardwood floor, a few exotic-looking rugs, and wood paneling on the walls. He … Continue reading →

Posted in arithmetic, challenges, logic, programming, puzzles | Tagged , , , , , | 15 Comments

Carnival of Mathematics #53

Posted on June 5, 2009 by Brent

Welcome to the 53rd Carnival of Mathematics! A somewhat shorter carnival this time, but I greatly enjoyed reading the submissions I did get, and I hope you do too. Meaghan Montrose at TutorFi presents ten tips for daily practicing your … Continue reading →

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Rational numbers and decimal expansions

Posted on September 7, 2008 by Brent

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 →

Posted in infinity, iteration, number theory, pattern | Tagged , , | 9 Comments