# If a irrational number be the basis of count

by Jhenrique
Tags: basis, irrational, number
 P: 686 In the comum sense, the number 10 is the base of the decimal system and is the more intuitive basis for make counts (certainly because the human being have 10 fingers). But, in the math, the number 10 is an horrible basis when compared with the constant e. You already thought if an irrational number can be the basis of system of count, it make sense?
 Mentor P: 18,333
P: 6,077
 Quote by Jhenrique In the comum sense, the number 10 is the base of the decimal system and is the more intuitive basis for make counts (certainly because the human being have 10 fingers). But, in the math, the number 10 is an horrible basis when compared with the constant e. You already thought if an irrational number can be the basis of system of count, it make sense?
Why is it horrible?

For arithmetic to work easily, the basis has to be an integer. It is hard to envision what a number would even look like with e or any non-integer.

Since computers became widespread, 8 or 16 might be practical alternatives to 10.

PF Gold
P: 3,686
If a irrational number be the basis of count

Have any of you folks ever converted everyday numbers to non-integer radixes?

I tried back in the late seventies, just out of curiosity but my math was not up to the challenge.
I wanted to see what would some of the physical constants, planck, c, μ0 , ε0, look like in bases e pi etc.

Closest i ever came was a Basic program that converted Florida's lotto numbers into 49 bit binary numbers and printed them out as hex, decimal and octal. No visual patterns emerged.

 For a non-integer radix β > 1, the value of x=d n.... d2d1 d0d-1d-2...d-m.... is x= βndn + β2d2 + β1d1 + β0d0 β-1d-1 +βmdm
Thanks !

old jim , who is distractable to a fault.
Mentor
P: 21,312
 Quote by mathman Why is it horrible? For arithmetic to work easily, the basis has to be an integer. It is hard to envision what a number would even look like with e or any non-integer. Since computers became widespread, 8 or 16 might be practical alternatives to 10.
Base-8 used to be used a lot, but not as much any more, as far as I can see. Base-2 (binary) and base-16 (hexadecimal) are heavily used in computer programming.
 Sci Advisor Thanks P: 3,759 Many years ago, when one of my daughters was in grade school... Over dinner she asked me what was the most "interesting" base for a number system. I answered ##-2##, because ##1+1=110## and you can get the rest of arithmetic from there. What I didn't know was that the question was prompted by a school homework assignment: Choose a radix and demonstrate worked addition, subtraction, multiplication, and long division problems in that radix. She pulled it off, although the long division algorithm is not deterministic - when dividing ##A## by ##B##, having ##nB\le{A}## and ##(n+1)B\gt{A}## doesn't mean that subtracting ##nB## is the right next step.