Article originally published 11/17/2013. Copyright, updating, and historical notes at end of article.
If you understand the everyday decimal (base 10) number system, then you already understand the duodecimal, base 12, dozenal counting and numbering system. You just don’t know you know yet. The complete lesson immediately follows the short introduction.
And at the end of the page is a video, What Is the Sound of Pi in Base 12. Kind of induces a strange feeling after awhile...
Timekeeping is heavily reliant on the number 12 and its composites (evenly divisible numbers: 2, 3, 4, 6).
How to Learn the Duodecimal, Dozenal, Base 12 Numbering System
An Interesting "Political" Side Note.
The base 12 numerical system, also known as the duodecimal or dozenal system, is just like all the other base numbering and counting systems. However, this is the only base numbering system which has a "political" aspect to it. This has to do with the number 12 being a very useful number and as to which symbols to use for the base 10 numbers "10" and "11".If one wishes to remain within the standardized structure of hexadecimal and the other base numbering and counting systems up to and including base 36, then the use of sequential numbers and letters should be used. Thus, as in hexadecimal, the base 10 number "10" is equal to the base 12 number "A", and the base 10 number "11" is equal to the base 12 number "B".
Others advocate the use of different symbols, some examples being:
 10 = T
 10 = X
 11 = E
Complete Lesson and Examples
A quick review of the decimal, base 10 structure...Base 10, Decimal Orders of Magnitude
1 · 10 · 100 · 1,000 · 10,000 · 100,000
Positional
100,000 · 10,000 · 1,000 · 100 · 10 · 1
We use the base 10 numbering/counting system in our daytoday living. Base 10 has ten numbers (09) and orders of magnitude that are times ten.
 The lowest order number represents itself times one.
 The next order number represents itself times 10.
 The next order number represents itself times 10 x 10, or itself times 100.
 The next order of magnitude would be 10 x 10 x 10, or 1000.
A base 10, decimal example would be the number 7824. This number means there are:
 Four 1’s,
 Two 10’s,
 Eight 100’s,
 And seven 1000's.
The duodecimal, base 12, dozenal numbering system...
...uses the same structure, the only difference being the orders of magnitude. Base 12 aka duodecimal has twelve numbers (0 thru B). The numbers are: 0 = 0, 1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 5, 6 = 6, 7 = 7, 8 = 8, 9 = 9
 A = 10
 B = 11
 The lowest order number represents itself times one.
 The next order number represents itself times 12. The next order number represents itself times 12 x 12, or itself times 144.
 The next order number represents itself times 12 x 12 x 12, or itself times 1728.
 The next order number represents itself times 12 x 12 x 12 x 12, or itself times 20736.
Duodecimal, Base 12 Orders of Magnitude
1 · 12 · 144 · 1728 · 20736 · 248832Positional
248832 · 20736 · 1728 · 144 · 12 · 1A basic, first example of a duodecimal number would be the base 12 number 11111. This would mean there is:
 one 1,
 one 12,
 one 144,
 one 1728,
 and one 20736.
Another base 12 example would be the number 2B9A. This number means there are:
 Ten 1’s,
 Nine 12’s,
 Eleven 144’s,
 And two 1728’s.
Another base 12 example would be the number A51B. This number means there are:
 Eleven 1’s,
 One 12,
 Five 144’s,
 And ten 1728’s.
Convenience relist...
Base 12, Duodecimal Orders of Magnitude1 · 12 · 144 · 1728 · 20736 · 248832
Positional
248832 · 20736 · 1728 · 144 · 12 · 1
Side notes...
 Latitude and longitude are heavily reliant on the number 12 and its multiples and composites.
 Dice probability theory loves the number 12 composites.
 Astrology, the zodiac, and ancient cultures recognized the uniqueness of the number 12.
More Duodecimal, Dozenal, Base 12 to Base 10 Conversion Examples
Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column. There is no significance attached as to where one column ends and the next one begins.
12 · 1

144 · 12 · 1

1728 · 144 · 12 · 1
 

0=0

92=110

B00=1584
 
1=1

100=144

BBB=1727
 
5=5

101=145

1000=1728
 
9=9

110=156

1001=1729
 
A=10

200=288

1010=1740
 
B=11

202=290

1100=1872
 
10=12

20A=298

1111=1885
 
11=13

20B=299

2000=3456
 
18=20

210=300

42BB=7343
 
20=24

7B6=1146

AB2B=18899
 
5A=70

A00=1440

B460=19656
 
5B=71

A2B=1475

BBBB=20735

Convenience relist...
Base 12, Duodecimal Orders of Magnitude1 · 12 · 144 · 1728 · 20736 · 248832
Positional
248832 · 20736 · 1728 · 144 · 12 · 1
The Dozenal Society of America has all sorts of information regarding the mathematical and societal aspects of the base twelve number, counting system.
What Is the Sound of Pi in Duodecimal
And last, but not least. Here is a video, The Sound of Pi in Base 12.
Copyright and Historical Information
This article was originally published on 11/17/2013 at a site called "hubpages". The article remained there for a few years and was then transferred to a site called "owlcation". The article remained at the second site for a few years. Both sites had and have severe platform management problems, thus the article has been moved here to websitewithnoname.com. This article is copyrighted. If anyone comes across a stolen copy, please let me know in the Comments Section below. Meanwhile, the article has been updated throughout the years to make it be the best that it can be; the iterations will continue.Some of the Comments From the Previous Platforms
 Commenter, Will Apse, said: I'm a bit weird about the number 12. As a kid I used pounds, shillings and pence for money with 12 pennies in the shilling and twenty shillings in the pound (decimalized when I was 12, lol). This might be why I often think about the oddities of 12's. Money and time are rather important.
 Commenter, DreamerMeg, said: I was brought up in the UK pre decimal money, same as Will Apse, but it's still difficult for me to get my head round the idea of base 12.
 Commenter, BradMastersOCcal, said: Binary to base 12 is not as clean as base 8 (3 bits) or 16 (4 bits); this allows binary to just overflow into the next number. Base 12 has to use 4 bits but stop at 1011 (B). It is more like BCD. I had no idea this was a popular common base. Thanks, it is a very interesting article.
 Commenter, DreamerMeg , said: As a child, we had to learn to count in 12's for the UK's monetary system. Counting in 10's is a lot easier. We had a class of 7yearolds chanting 12 pence is 1 shilling, 18 pence is 1 and sixpence, 24 pence are two shillings, 30 pence is 2 and sixpence, 36 pence is three shillings! The UK went decimal in 1971 but I can still calculate between new money and old money and between decimal measurement systems (SI units) and the old pounds and ounces. Keeps the brain active but I don't know that it's useful. Good article.
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