Express 4.54545454545... as a rational number, in the form pq where p and q are positive integers with no common factors.

Answer:the final answer is 50/11Step-by-step explanation:Here let's regard the first number of this geometric series as 0.54, holding the 4 to include later.  The next is 0.0054, the next 0.000054, and so on.Thus, the common ratio is 1/100.  Then the sum of the infinite series, not including that 4, is    a          0.54        0.54-------- = ------------ = ------------  1 - r       1 - 1/100     99/100                                                                                       54Multiplying both 0.54 and 99/100 by 100 results in ------- and this                                                                                         99     0.545454....Now add the 4 back in, obtaining 4  54/99, or (396 + 54) / 99.This is the same as 450 / 99.  You can readily check with a calculator to see whether this is equivalent to the given   4.54545454545...Note that 450/99 is in the form p/q (not pq), where p and q are positive integers.  But also note that 450/99 can be reduced to 150/33, or50/11.  A calculator will show you that 50/11 is equivalent to the given   4.54545454545...Hence, the final answer is 50/11 (in the form p/q, NOT pq).