Wrong Answer - Rewrite Rational Number as a Fraction. This number 2.962962 can be rational
$$x=2.962962$$
$$10x=29.62962$$
$$100x=296.2962$$
$$1000x=2962.962$$
$$1000x-10x=\frac{990x}{990}=\frac{2933}{990}$$
why is this wrong?
That way of getting the answer is how I was said to do it
Comment:
$$1000x-x=\frac{999x}{999}=\frac{2960}{999}=?$$
 A: I assume you meant a repeating decimal like $2.\overline{962}$ (i.e. $2.9629629\ldots$) rather than one that terminates like you write.
Your work at the end is somewhat confused; I can't tell what you were trying to do. But the calculation of $1000x - 10x$ yields
$$ \begin{matrix}
2&9&\not 6^5&{}^1 2&.&9&\not6^5&{}^1 2&9&\not6^5&{}^12&...
\\ & & 2&9&.&6&2&9&6&2&9&...
\\\hline
\\ 2 & 9 & 3 & 3 & . & 3 & 3 & 3 & 3 & 3 & 3 & \cdots
\end{matrix} $$
(I hope that is how they still notate subtraction these days) and so you have
$$ 1000 x - 10 x = 2933 + \frac{1}{3} $$
and
$$ 1000 x - 10 x = 990 x $$
and so we've derived
$$ 990 x = 2933 + \frac{1}{3} $$

Of course, it would have been easier to compare $1000x$ to $x$....
A: $$
1000x -x = 2962.962962\ldots - 2.962962\ldots = 2960.
$$
The fractional part cancels out completely.
Then
$$
x = \frac{2960}{999} = \frac{37\cdot80}{37\cdot27} = \frac{80}{27}.
$$
A: Hint: there's a very easy way to transform periodic into decimals without any calculation.  Here's an example:
$$0.123\overline{4567}=\frac{1234567-123}{9999000}.$$
In your case it's just 
$$2\frac{962}{999}.$$
A: The number $2.962962$ certainly is rational, because $$2.962962 = \frac {2962962}{1000000}$$
BUT... if you mean $2.962962\ldots$, supposed to mean $2.962\overline{962} = 2.\overline{962}$, then $$1000\cdot 2.\overline{962} = 2962.\overline{962}$$ so 
$$1000\cdot 2.\overline{962} - 2.\overline{962} = 2960$$ thus $$999\cdot 2.\overline{962} = 2960$$ and $$2.\overline{962} = \frac {2960}{999}$$ 
