interesting question ! :)
I THINK THIS A POSITIONAL NUMBER SYSTEM .and that's of great advantage ..simple shifting the position of decimal . this is the most conventional answer ..! but somehow it seems , not that strong . we could have tried to construct a fractional system in other number systems as well !
but there are certain points i have made out :
if the base is more than 10 , say 20 . then if you want to use our 10 symbols (i.e. 0, 1..,9) it not possible for us to write numbers more than 9 and less than 20 or numbers more than 189 and less than 200 and numbers of similar form ) , so in that case for each unit either you will have to allot two places for digits (which will make it difficult to read a number) or you will have introduce more 10 symbols , which will make it more complex and we wont get any advantage. cause 20 is just a a multiple of 10 by 2 ..and 2 is a factor of 10 ( if the base would be 30 then , we could take it as an advantage that the problem in fixing the decimal we face while handling division by 3 could be simplified . but in that case just imagine how many symbols you will have to introduce !!! the base could be 12 . in that case dividing by three would not face any approximation problem..or if the base would be 14 then we would easily be able to divide by 7 ..but in both 12 and 14 base the problem in dividing by 5 arises. and in ancient days as our hand and toe consists of 5 fingers , i think divisibility ease for 5 was given preference ) so among systems with 10 or more than ten , the base 10 system , i.e. decimal system was given preference in different civilization , as a human mind always and everywhere think in the same direction and following our ancestors we set this as our ruling international number system mostly used !
- now , for bases less than 10 : there is no number which has three prime factors ! among numbers 10 or less than 10 , 10 has the highest number of one digit-ed prime factors ! and for that reason in decimal system , we can properly divide any number by most number of numbers compared to all the other systems with base less than 10 .!(except 6 . which was again given less priority because 10 is a multiple of 5 )
NOTE : some say , "you can order the numbers with specific space between in decimal system .. If we can't order the number with equal interval among them , then it wont be possible to get any number line,and whole number theory will possibly be collapse then . the way co-ordinate geometry ,..vector algebra work , where ordering is very important will collapse ..! e.g in octal system 63 =77 where 64 = 100 and 65 = 101 ..so , then what's the measure of unit countable increase ? .." but , that's not a proper argument in my opinion . there we will have to consider 77+1 = 100 , 7+1=10 , 777+1=1000...and so on ,..