<PRE><B>Question 1108765</B>
&lt;br&gt;
Ignore the whole number part and convert the repeating decimal; then add the whole number part back into the answer.&lt;br&gt;
Slow, formal algebraic method....&lt;br&gt;
Call the number x.  Then, since 2 digits are repeating, multiply x by 100 and subtract x from the result.  The repeating digits will line up and are cancelled by the subtraction.&lt;br&gt;
{{{100x = 23.4343434}}}
{{{x = .2343434}}}
{{{99x = 23.2}}}
{{{990x = 232}}}
{{{x = 232/990 = 116/495}}}&lt;br&gt;
Then the final answer is the mixed number 1 116/495; or, if an improper fraction answer is asked for, {{{(495+116)/495 = 611/495}}}.&lt;br&gt;
Shortcut....&lt;br&gt;
Write out on paper the process shown above to see how this shortcut works....&lt;br&gt;
The denominator of the fraction in unsimplified form is 990, because there are two digits that repeat and one digit that does not repeat.  In general, the denominator is one 9 for each repeating digit followed by one 0 for each non-repeating digit.&lt;br&gt;
The numerator of the fraction is (the non-repeating digits plus one cycle of the repeating digits) minus (the non-repeating digits) -- in your example, &quot;234 - 2&quot;.&lt;br&gt;
So without going through all the formal algebra shown earlier, you can just write down the (unsimplified) answer:&lt;br&gt;
{{{(234-2)/990 = 232/990}}}</PRE>