Are some infinite fractions in one counting system non-infinite in

anginih86

anginih86

Answered question

2022-06-21

Are some infinite fractions in one counting system non-infinite in another?
I'm curious whether some infinite periodic fractions in one counting system (e.g. decimal - 10/3 = 3.33333...) turn out to be non-infinite in another system and vice - versa.
Please excuse me if my terminology is not 100% accurate.

Answer & Explanation

ejigaboo8y

ejigaboo8y

Beginner2022-06-22Added 29 answers

Yes.
10 10 / 3 = 3 1 3 = 10.1 3 , for instance.
Basically, if the denominator divides a sufficiently high power of the base, then the radix representation will terminate.
For example, 128 | 10 7 so 1 128 10 terminates in base 10 but continues forever in base 3.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?