SOLUTION: I want to double check to make sure that I did this problem right or did I misunderstand the question. Convert the repeating decimal 0.1212...to a fraction with integer numerato

Algebra ->  Decimal-numbers -> SOLUTION: I want to double check to make sure that I did this problem right or did I misunderstand the question. Convert the repeating decimal 0.1212...to a fraction with integer numerato      Log On


   

Question 167100This question is from textbook
: I want to double check to make sure that I did this problem right or did I misunderstand the question.
Convert the repeating decimal 0.1212...to a fraction with integer numerator and demoninator.
1/10 + 2/100 + 1/1000 + 2/10,000
(1,000 + 200 + 10 + 2)/10,000 = 1,212/10,000
I then divided by 2 to simplify which = 606/5000
" " = 303/2500 being the final answer
This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, nice try, but your answer of 303%2F2500+=+0.1212 and this is a terminating (non-repeating) decimal! You can check this in your calculator.
Here's the way to convert this repeating decimal to a fraction:
Let n = 0.1212... Multiply both sides by 100 to get:
100n = 12.1212... Now subtract n = 0.1212...
100n-n = (12.1212...)-(0.1212...) Perform the indicated subtraction.
99n = 12 Finally divide both sides by 99.
n+=+12%2F99 substitute n = 0.1212...
0.1212... = 12%2F99 Reduce the fraction.
0.1212... = 4%2F33