1
vote
2answers
80 views

most efficient way to convert a number into a fraction

supposing I have a decimal like $$ 0.30000000000000027$$ What would be the best way to know the same number but in a fraction way like we know $\dfrac{1}{3} > 0.30 > \dfrac{1}{4}$ because ...
5
votes
1answer
140 views

finite field to rational fraction

Suppose I have a number $n\in\mathbb F_p$, i.e. an element of the finite field obtained by arithmetic modulo some (odd) prime $p$. I'm looking for a way to find a simple description of $n$ as a ...
1
vote
1answer
79 views

How to chose a rational with a non-repeating fractional part in an arbitrary base?

How can I choose an $x\in[a,b)\subseteq[0,1)$, where $a,b\in\mathbb{Q}$, such that $x$ has a non-repeating fractional part in some chosen base? For example, say I'm looking at ...
6
votes
1answer
459 views

Faster arithmetic with finite continued fractions

I was curious about different representations of rational numbers and came across the finite continued fraction (see wp:Finite_continued_fractions ). Note: I will refer to traditional rational ...
3
votes
3answers
544 views

How to find a “simple” fraction between two other fractions?

If we have two fractions $a = { a_1 \over a_2} $ and $c = {c_1 \over c_2}$ with $a<c$, how to find the fraction $b = { b_1 \over b_2 }$ , $a < b < c$ for which some measure of ...