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Medicare was billed 3.62 mg of a drug expressed with a code description of .1 mg per unit (in other words we billed 37 units of the code, because we rounded up). Medicare says if the dosage given is not a multiple of the number provided in the code description, the provider shall round up to the nearest whole number in order to express then number as a multiple. I'm not sure if we should round up or down. I think 3.62 is a multiple of .1 but when you divide 3.62 by .1 there's a remainder of .2. Even though there's a remainder it is evenly divisible. So I'm confused.

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    $3.62/0.1=36.2\approx 36$2017-02-23
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    What is the definition of a multiple?2017-02-23
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    $3.62=36\times0.1+0.02$. Since $0.02>0$, it gets rounded to $0.1$ (the rules laid out by medicare) so $3.62$ is rounded to $3.6+.1=3.7$2017-02-23
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    What do you mean by "evenly divisible"?2017-02-23

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That translates to a multiple

$$ k = \lceil m / 0.1 \text{mg} \rceil $$ and a dosage $$ m' = k \cdot 0.1 \text{mg} $$

For your example $m = 3.62 \text{mg}$ we get $k = 37$ and $m' = 3.7 \text{mg}$.

The remainder $0.02 \text{mg} = (1/5) \cdot 0.1 \text{mg}$ was rounded up to a full unit of $0.1 \text{mg}$.