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I have a situation like this:

$3\times 10^n$ and $4\times 10^m$ and $a\times 10^p$ are all in standard form. $\frac{3\times 10^n}{4\times 10^m} = a\times 10^p.$

Is it possible to calculate the value of $a$ only by using the above equation and no further data? And if so what is the value of $a$?

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    In my neck of the woods, your "standard form" is our "scientific notation".2011-04-24

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You have $\frac{3\times 10^n}{4\times 10^m} = 0.75\times 10^{n-m}.$ If by "standard form" you mean that the the number $a$ must be between $1$ and $10$, strictly less than $10$, then $a = 7.5$ with $p=n-m+1$