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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.

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3 Answers 3

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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 $22,48,98$.

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If $r$ is a real number, $r$ mod $1$ is the fractional part of $r$. It can also be written $\{r\}$.

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This is a notation of the fractional part of the expression.

See:http://en.wikipedia.org/wiki/Fractional_part

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