I was going over a paper regarding linear algebra and its relation to chaos. One particular section focuses on Arnold's cat map. It briefly mention modular arithmetic.
In this case, it dealt with the generic form of $x \hspace{1mm} mod \hspace{1mm} 1$.
More specifically, $x \hspace{1mm} mod \hspace{1mm} 1$ denotes the unique number in the interval $[0,1)$ that differes from $x$ by an integer.
That said, the paper gave a few examples:
$2.3 \hspace{1mm} mod \hspace{1mm} 1 = 0.3$
$0.9\hspace{1mm}mod \hspace{1mm}1 = 0.9$
$-3.7\hspace{1mm}mod\hspace{1mm}1 = 0.3$
$2.0\hspace{1mm}mod\hspace{1mm}1 = 0$
$(2.3, -7.9)\hspace{1mm}mod\hspace{1mm}1 = (0.3, 0.1)$
Based on those examples, what is the fundamental reason behind $0.9\hspace{1mm}mod \hspace{1mm}1 \hspace{1mm} equaling \hspace{1mm} 0.9$ and $0.3\hspace{1mm}mod \hspace{1mm}1 \hspace{1mm} equaling \hspace{1mm} 0.3$? In more detail, why couldn't the latter statement be equal to $0.7$?
Obviously, that isn't the answer, but is it a concept similar to why we round 7.5 up to 8 (i.e. the 0.5)?