- #1
pseudogenius
- 7
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I have been playing around with numbers in different bases and then I thought, what if they were in fractional bases. I found a way to convert numbers to fractional bases and have been searching on the internet and not found a similar way to do this. Anyway, here is an example of how I would do this:
The problem is: Write 5 in base 3/2
5*(2/3)= 3 remainder 1
6*(2/3)= 2 remainder 0
2*(2/3)= 1 remainder 1
1*(2/3)= 0 remainder 2
Take 2101 and divide each digit by 2.
5 in base 3/2 = 2/2 1/2 0/2 1/2
Check:
(2/2)*(3/2)^3+(1/2)*(3/2)^2+(0/2)*(3/2)^1+(1/2)*(3/2)^0=
27/8+9/8+0+1/2= 5
It worked.
Is it okay to extend digits to rational digits?
Is this a valid way to put integers in rational bases?
I have worked out a way to put rational numbers into rational bases but the process is complicated.
The problem is: Write 5 in base 3/2
5*(2/3)= 3 remainder 1
6*(2/3)= 2 remainder 0
2*(2/3)= 1 remainder 1
1*(2/3)= 0 remainder 2
Take 2101 and divide each digit by 2.
5 in base 3/2 = 2/2 1/2 0/2 1/2
Check:
(2/2)*(3/2)^3+(1/2)*(3/2)^2+(0/2)*(3/2)^1+(1/2)*(3/2)^0=
27/8+9/8+0+1/2= 5
It worked.
Is it okay to extend digits to rational digits?
Is this a valid way to put integers in rational bases?
I have worked out a way to put rational numbers into rational bases but the process is complicated.