I am submitting this question here because I don't know where else to put it.

My question concerns the use of number systems other than base 10.  Specifically, how to express a non-integer in a base other than ten.


Example:  How does one express the number 4.5 in base 8?   From an abundance of ignorance, I reason that in base 10,  4.5 means 4 plus 5/10 .  Therefore shouldn't 4.5 base 8 mean 4 plus 5/8? 

And, shouldn't 4.5 base 10 be equal to 4.4 base 8? Or, is some other notation used for non-integers in bases other than ten? 

And, what about base 7?  What would the equivalent of 4.5 base 10 in base 7 be?  4. 3.5???  but 3.5 also in base seven must equal 3. 3.5 and, uh.... hmm.

Further:  how would a scientist from another planet (the 'people' there have just four digits on either 'hand') on which base 8 was used express the number pi  ?  It would still be the ratio of the circumference and the diameter of a circle (assuming earth-like geometry) wouldn't it?  Would pi base 8 be a non-ending 'decimal' number?   3 point what?

Also, how is the number pi expressed in binary?  Or, for that matter, how is any non-integer expressed in binary?  Surely 'whole' numbers aren't restricted to base 10, are they?

As I say, I am nearly totally ignorant of this and would appreciate any insights.

Jack Murd

Thanks
Jack.

Last edited by JackMurd (2006-08-06 23:16:35)