TITLE: What is the meaning of $x*\sqrt{3} \mod 1$?
QUESTION [5 upvotes]: What is the meaning of $x*\sqrt{3} \mod 1$? 
I'm trying to understand this:
$$5( x*\sqrt{3} \mod 1) $$
If we talk about: $x=19,22,48,98$ what will be the result?      
I don't know how to calculate it.

REPLY [3 votes]: For all $n\in\mathbb{R}$, $n\mod 1$ is fractional part of $n$ (for example: if $n=3.14$ then $n\mod 1=3.14\mod1=\{3.14\}=0.14$). In this case
$$5(x\sqrt3\mod1)$$
for $x=19$ it will be
$$5(19\sqrt3\mod1)\approx5(32.909\mod1)=5\cdot0.909=4.545$$
Similar, you can do it for $22,48,98$.