Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

We can write any $x\in\mathbb R$ as its $b>1\in \mathbb N$ basis expansion:

$$x=sgn(x)\sum_{d=-\infty}^\infty b^d \lfloor |x|b^{-d} - b\lfloor |x|b^{-d-1} \rfloor \rfloor$$

Can one come with the same kind of explicit expansion that would be valid for any rational $b=p/q$?

share|cite|improve this question

1 Answer 1

up vote 0 down vote accepted

Yes; this is known as Non-integer representation or $\beta$-expansion.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.