The AltMBA. The most successful online workshop of its kind. Read these two articles The Marketing Seminar. Seth is an entrepreneur, best-selling author, and speaker. Though renowned for his writing and speaking, Seth also founded two companies, Squidoo and Yoyodyne acquired by Yahoo! By focusing on everything from effective marketing and leadership, to the spread of ideas and changing everything, Seth has been able to motivate and inspire countless people around the world.

In an astonishing turn of events, in May , he was inducted into the Marketing Hall of Fame as well. He might be the only person in both. Check it out here. Seth rarely does long-haul travel, but to inquire about hiring Seth to speak, drop him an email. There's no active tweeting, but you can find his daily post republished at thisissethsblog. Seth's Rider.

This document will save you time and save me hassle, we both win. Four articles to read before having your next meeting. These four articles can make things better for everyone, especially the organizer. Consider the Akimbo. Read, Watch, Learn Books, Courses and More. Also see: Daddy, Papa, and Me. Stella Brings the Family. Miriam B.

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Fortunately, Stella finds a unique solution to her party problem in this sweet story about love, acceptance, and the true meaning of family. A Tale of Two Daddies. Vanita Oelschlager. Also see: A Tale of Two Mommies. Sarah S. Pre-K — 1 Everyone is happy but the young girl who fears losing her favorite uncle when he gets married —— until she sees she is really gaining a new uncle. The Best Man. Richard Peck. Starts with a wedding disaster and ends with a great one. Dan Pilkey. Harold is pictured with his husband and their kids.

Luv Ya Bunches. Lauren Myracle. Four diverse 5th grade girls come together in friendship.

One of the girls has two moms. The Magic Misfits. Neil Patrick Harris. Carter finds friends and magic saving the town of Mineral Wells from B.

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Bosso's villainous clutches. The Misadventures of the Family Fletcher. Dana Alison Levy.

## NSTA Science Store :: More Picture-Perfect Science Assembled Book Collection :: NSTA Press Book

Meet the Fletchers: four boys, two dads, and one new neighbor who just might ruin everything. The Phantom Unicorn City Kids 4. Zetta Elliott. When a medieval tapestry comes to life in a nearby museum, Q must face his fears and battle a villain who has waited five hundred years to destroy the world. Amy Ignatow.

Julie has two dads. To use them, the given number must first be decomposed into a sum of numbers with only one significant digit each. For example:. This decomposition works the same no matter what base the number is expressed in. Just isolate each non-zero digit, padding them with as many zeros as necessary to preserve their respective place values. If the digits in the given number include zeroes for example, , Then the digit conversion tables can be used to obtain the equivalent value in the target base for each digit.

If the given number is in duodecimal and the target base is decimal, we get:. Now, because the summands are already converted to base ten, the usual decimal arithmetic is used to perform the addition and recompose the number, arriving at the conversion result:. That is, duodecimal , If the given number is in decimal and the target base is duodecimal, the method is basically same. Using the digit conversion tables:.

However, in order to do this sum and recompose the number, now the addition tables for the duodecimal system have to be used, instead of the addition tables for decimal most people are already familiar with, because the summands are now in base twelve and so the arithmetic with them has to be in duodecimal as well. Doing the arithmetic properly in duodecimal, one gets the result:. That is, decimal , This section is about the divisibility rules in duodecimal. To test for divisibility by 5, double the units digit and subtract the result from the number formed by the rest of the digits.

## Duodecimal

If the result is divisible by 5 then the given number is divisible by 5. To test for divisibility by 5, subtract the units digit and triple of the result to the number formed by the rest of the digits. Form the alternating sum of blocks of two from right to left. To test for divisibility by 7, triple the units digit and add the result to the number formed by the rest of the digits. If the result is divisible by 7 then the given number is divisible by 7.

To test for divisibility by 7, subtract the units digit and double the result from the number formed by the rest of the digits. To test for divisibility by 7, 4 times the units digit and subtract the result from the number formed by the rest of the digits. Form the alternating sum of blocks of three from right to left. If the 2-digit number formed by the last 2 digits of the given number is divisible by 8 then the given number is divisible by 8.

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If the 2-digit number formed by the last 2 digits of the given number is divisible by 9 then the given number is divisible by 9. Sum the alternate digits and subtract the sums. If the result is divisible by 11 the number is divisible by 11 the equivalent of divisibility by eleven in decimal. If the 2-digit number formed by the last 2 digits of the given number is divisible by 14 then the given number is divisible by Duodecimal fractions may be simple:. As explained in recurring decimals , whenever an irreducible fraction is written in radix point notation in any base, the fraction can be expressed exactly terminates if and only if all the prime factors of its denominator are also prime factors of the base.

The number of denominators which give terminating fractions within a given number of digits, say n , in a base b is the number of factors divisors of b n , the n th power of the base b although this includes the divisor 1, which does not produce fractions when used as the denominator.

### BETTER BY THE DOZEN, PLUS TWO

The number of factors of b n is given using its prime factorization. The number of divisors is found by adding one to each exponent of each prime and multiplying the resulting quantities together. The Dozenal Society of America argues that factors of 3 are more commonly encountered in real-life division problems than factors of 5.

Advocates of duodecimal systems argue that this is particularly true of financial calculations, in which the twelve months of the year often enter into calculations. However, when recurring fractions do occur in duodecimal notation, they are less likely to have a very short period than in decimal notation, because 12 twelve is between two prime numbers , 11 eleven and 13 thirteen , whereas ten is adjacent to the composite number 9. Nonetheless, having a shorter or longer period doesn't help the main inconvenience that one does not get a finite representation for such fractions in the given base so rounding , which introduces inexactitude, is necessary to handle them in calculations , and overall one is more likely to have to deal with infinite recurring digits when fractions are expressed in decimal than in duodecimal, because one out of every three consecutive numbers contains the prime factor 3 in its factorization, whereas only one out of every five contains the prime factor 5.

All other prime factors, except 2, are not shared by either ten or twelve, so they do not influence the relative likeliness of encountering recurring digits any irreducible fraction that contains any of these other factors in its denominator will recur in either base. Also, the prime factor 2 appears twice in the factorization of twelve, whereas only once in the factorization of ten; which means that most fractions whose denominators are powers of two will have a shorter, more convenient terminating representation in duodecimal than in decimal representation e.

The representations of irrational numbers in any positional number system including decimal and duodecimal neither terminate nor repeat. The following table gives the first digits for some important algebraic and transcendental numbers in both decimal and duodecimal. From Wikipedia, the free encyclopedia. Not to be confused with Dewey Decimal Classification or Duodecimo. Aitken, The Case Against Decimalisation [27].