Expert: Paul Klarreich - 6/24/2010

Question
Greetings,
Is it possible to have numbers in fractional bases?Just like you have numbers in base 2,10,16 and so on.Can you have numbers in base 1/2 ,1/3 and so on?In base 2 the only bits possible are 1 and 0.In base 1/5 for example what "digits" are allowed? Thanks

Answer
Questioner: jay
Country: Gambia
Category: Advanced Math
Private: No
Subject: fractional bases
Question: Greetings,
Is it possible to have numbers in fractional bases?Just like you have numbers in base 2,10,16 and so on.Can you have numbers in base 1/2 ,1/3 and so on?In base 2 the only bits possible are 1 and 0.In base 1/5 for example what "digits" are allowed? Thanks
..............................................
Yes, but they would be fractions:

453 (base 1/7) would mean:

3 * 1/7 + 5*(1/7)^2 + 4 * 1/7)^3

I don't think it is particularly useful, since you can always use negative exponents with ordinary (integer) bases.