# What are the advantages of using a base 15 number system such as used by the Hela (Huli people) of Papua New Guinea?

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The higher the base of the number system determines how many digits are needed to count big numbers, e.g. binary (base 2) takes 10 digits (bits) for 1000, decimal (base 10) takes 3 digits and hexadecimal can go up to 4,096 with 3 digits. This is why passwords require letters and such, so the base is very large (10 digits, 26 lowercase, 26 uppercase and a bunch of symbols). So having a relatively large base would help them deal with larger numbers.

But the real reason for the base is the convenience of going up a digit. In binary, moving the decimal point (e.g. 1 to 10) doubles the value of the number. Decimal corresponds to our fingers. Dozens was seen as convenient since they could be divided evenly into three or four groups (which make up a vast amount of small numbers). My guess is that 15 is similar to that since is can be broken into groups of 3 or 5.

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• Two advantages of a base 15 number system over a base 10 number system is that generally fewer digits are required to represent numbers, and thirds can be easily represented as terminating "decimals" (one-third is 0.5 in base 15, but one-third is 0.33333... in base 10).

There are disadvantages as well. Computing in base 15 requires knowing a greater number of addition and multiplication facts than computing in base 10, and halves cannot be represented as terminating "decimals" (one-half is 0.77777... in base 15, but one-half is 0.5 in base 10).

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