What is 9.09 repeating (if the 0 and 9 are both repeating) as a fraction? Like 9.090909090909... as a fraction. Thanks to anyone who can help :3

1 Answer
Oct 12, 2017

100/11

Explanation:

Setting the number over 9, 99, 999, etc. will give you repeating decimals for that many places.

Since both the 10ths and 100ths place is repeating (.bar(09)), then we can represent that part of the number as 9/99=1/11

Now we just have to add 9 and represent the sum as a fraction:

9+1/11=99/11+1/11=100/11