Can we write bar35 or (353535.....) In form of p/q where q is not equal to 0 ? Thanks
1 Answer
Apr 22, 2018
Explanation:
In Socratic we can write 0.overline{35} between hashtag signs and it renders as
That's pretty nice. I found it by trying some LaTeX, whose features have been partially adapted.
Turning to the problem, whenever we have a purely repeating decimal like this, where the repeating part starts right after the decimal point, we quickly get the fraction by just adding a denominator of nines whose length is the length of the repeating part.
That's nice for quickly getting the answer, but why does it work? It works because a purely repeating decimal is really a geometric series in disguise, and the same trick for adding up a geometric series works for a repeating decimal:
