Three numbers that multiply to ten (It gets harder) I am working on a problem that involves the following:
One must find three numbers, integers and/or decimals, that multiply to ten. 
Here's the catch:
You must use all integers, $0-9$, in the answer! So $1\times 2\times 5$ does not work.
I do not want the answer.
Instead, I ask if anyone has any ideas to which I can get as close to 10 as possible. The hint in the problem is that you cannot get to ten exactly, but close to it. 
Right now, I have $1\times 2\times 5.0346789 = 10.0...$ Again, I do not want the answer, only a mathematical way to get to the answer. I cannot determine why I would be assigned this problem if it had no relation to mathematics.
Decimals ($\rm0.xxx$) count as use of the $0$, and you can place the zero at the end ($\rm x.xxx0$), too
 A: You could try programming a search that factors integers that are close to powers of $10$, and then examines the factors for their digits.  
For example, $100002$ factors as $2\times3\times7\times2381$.  Searching through possible triples of divisors, $6\times7\times 2381$ has unique digits (but is missing $4$, $5$, and $9$).  If all digits were accounted for, this would lead to to $10.002=6\times7\times0.02381$.  
(I'm not sure from your post if you are allowed to repeat digits, like how $0$ is repeated in this example.)
The search parameters would be which powers of $10$ you would examine, and also constraints on how far away from that power of $10$ you would roam.  If digits aren't supposed to be repeated, I think $10^a$ with $a$ in $\left\{9,10,11\right\}$ would be appropriate.  (And at this level, factoring shouldn't take the program too long.)
A: So, you've started with $1\times2\times5$, and you've varied the 5 a little bit. Maybe you could try varying two of the three numbers, or all three of them. 
