Question

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

Answer 1

`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`