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

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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

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Answer 1 · 2017-10-12T22:57:13

$\frac{100}{11}$ $100/11$

Explanation:

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

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

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

$9 + \frac{1}{11} = \frac{99}{11} + \frac{1}{11} = \frac{100}{11}$ $9+1/11=99/11+1/11=100/11$

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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

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