Question 1188231
<pre>
Since you posted this in the Sequences-and-series section, maybe you wanted to
see it done as an infinite geometric series:

2 + .045
  + .000045
  + .000000045
  + ...........

2 + 0.045 + 0.000045 + 0.000000045 + ...

2 + 4.5x10<sup>-2</sup> + 4.5x10<sup>-5</sup> + 4.5x10<sup>-8</sup> + ...

The terms to the right of 2 form an infinite geometric series with first term =
a<sub>1</sub> = 4.5x10<sup>-2</sup> and common ratio r = 10<sup>-3</sup>

{{{S[infinity]}}}{{{""=""}}}{{{a[1]/(1-r)[""]}}}

{{{S[infinity]}}}{{{""=""}}}{{{(4.5*10^(-2))/(1-10^(-3))[""]}}}

Multiply numerator and denominator by 10<sup>3</sup>

{{{S[infinity]}}}{{{""=""}}}{{{((4.5*10^(-2))*10^3)/((1-10^(-3))*(10^3))[""]}}}{{{""=""}}}{{{(4.5*10^1)/(10^3-10^0)}}}{{{""=""}}}{{{45/(1000-1)}}}{{{""=""}}}

{{{45/999}}}{{{""=""}}}{{{5/111}}}

So the fraction is {{{2&5/111}}} or {{{227/11}}}

Edwin</pre>