How to convert Repeating Decimals Into Fractions

It is fairly easy to take a fraction and turn it into a repeating decimal by hand. This is simple division.<p>But being able to go in the other direction and turn a repeating decimal into a fraction would be a cool party trick.<p>Let us take "0.454545454545..." to illustrate the trick.<p>Simply take the number that repeats, in this case 45, and divide it by however many 9's as there are digits in the original number. Since 45 is 2 digits, then divide 45 by 99.<p>Now, 45/99 simplifies down to 5/11.<p>So, "0.454545454545..." = 5/11 http://mathema-tricks.blogspot.com/