Quote History Quoted:
.500, .333, .250, .167
Don't make this harder than it needs to be.
Of all places to use a fraction, probably the 2nd most notable (behind 1/3) is Pi, 22/7, and it's taught as a decimal.
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But, in base twelve, 1/2 is 0.6, 1/3 is 0.4 (no repeating for ever), 1/4 is 0.3, and 1/6 is 0.2, etc. It does simplify common fractions. The only better base (but more cumbersome) is base 24 to reduce repeating decimals for common fractions.
Also, pi is not a fraction. It is the ratio of the circumference of a circle to its diameter. It is irrational, meaning there is no expressible ratio in numerical form. The fraction 22/7 is an approximation that in many cases is close enough. But, still there are other fractions that are closer, but do not quite get to an actual value.
In addition, to divide a line segment into 10 parts is also more difficult with just a compass (divider) than it is to divide into 12 parts. Sixteen parts is even easier, and is why we have pounds, ounces, and drams.
If you want to divide things into 10 parts each, there is the metric system. Which, does have plenty of nice features. Still, I think that Napoleon screwed up with it by not using base 12 (add the numbers dec and el for 10 and 11 respectively), and not basing the unit of length on the acceleration of gravity. Imagine if the acceleration of gravity (on earth) were 12 meters per second squared, and that the meter divided into 12 parts, and each of those divided into 12 as well. Then the unit of mass would follow the same principle with the base unit of mass (the gram) being 1/12 of a meter cubed. Science would be even easier than with the current metric system.
ETA, in base twelve, the word for twelve is "Doe", so you count one, two, . . . , dec, el, doe. I'm no sure on how to get the symbols for dec and el on computer (I'm sure they are there in a character map somewhere).