(41) Round To The Nearest 1/n

[Dieter]

(04-14-2018 08:09 PM)Mike (Stgt) Wrote:  For positive n do doubt. Same for negative n? Sure? How did you prove that?

Simple. We are looking for a value of z for which z/n is as close to x as possible. The program then returns z/n. If n<0 then z has to have the opposite sign of x.

In simple words: z has to be an integer, but it doesn't have to be a natural number.
In our example \(\pi\) rounded to the nearest –1/16 is 3,125, which is –49/–16. Or z=–49.
The essential point here: \(z\in\mathbb{Z}\) and not only \(z\in\mathbb{N}\).

On the other hand –3,125 cannot be the correct answer as it isn't the closest –1/16 at all. Even 0 is closer to \(\pi\) than –3,125. ;-)

Dieter