Question 1188231
<pre>
N = 2.045045045...

<pre>
On the right, move the decimal just to the right of the end of the first cycle
of repeating digits, multiply the left side by the power of 10 corresponding to
the moving of the decimal on the right.

In other words, multiply both sides by 1000

1000N = 2045.045045045...

Subtract the original equation

1000N = 2045.045045045...
    N =    2.045045945...
-------------------------
 999N = 2043
    N = 2043/999
    N = 227/111

Edwin</pre>