Question 1207585
<br>
Do some long division in base 16 ("2" base 16 divided by "11" base 16) and verify the result.<br><pre>

      -----------------
   11 ) 2. 0 0 0 0 ...


           1
      -----------------
   11 ) 2. 0 0 0 0 ...
        1  1
        -------------
           F 0


           1 E
      -----------------
   11 ) 2. 0 0 0 0 ...
        1  1
        -------------
           F 0
           E E
           ---------
             2 0</pre>
The remainder is the same number we started with, so the digits "1E" will repeat.<br>
ANSWER: 0.1E1E1<br>
Check to see that this hexadecimal is equal to 2/17:<br>
0.1E1E1E... base 16 = ...<br>
{{{1/16+14/16^2+1/16^3+14/16^4}}}+...<br>
{{{(1/16+14/16^2)+(1/16^2)(1/16+14/16^2)}}}+...<br>
{{{(16/16^2+14/16^2)+(1/256)(16/16^2+14/16^2)}}}+...<br>
{{{(30/16^2)+(1/256)(30/16^2)}}}+...<br>
Use the formula for the sum of an infinite geometric sequence...<br>
{{{(30/16^2)/(1-1/16^2)=(30/16^2)/(255/16^2)=(30/255)=(2/17)}}}<br>