To convert the decimal \( 0.09 \) into a fraction, we can recognize that it can be expressed as:
\[ 0.09 = \frac{9}{100} \]
Now, we can simplify the fraction \( \frac{9}{100} \). The greatest common divisor (GCD) of 9 and 100 is 1, meaning \( \frac{9}{100} \) is already in its simplest form.
However, your options suggest that we may need to express \( 0.09 \) as a fraction equivalent to one of the listed choices.
If we analyze further, we can see that:
- The decimal \( 0.09 \) can also be expressed as \( \frac{9}{100} \) but it does not correspond directly to \( \frac{1}{90} \), \( \frac{1}{11} \), or \( \frac{1}{9} \).
- The fraction \( \frac{1}{90} \) is approximately \( 0.0111...\), not \( 0.09 \).
- The fraction \( \frac{1}{11} \) is approximately \( 0.0909...\), but does not exactly match \( 0.09 \).
- The fraction \( \frac{1}{9} \) is approximately \( 0.111...\), also not matching.
Thus, none of these options directly correspond to \( 0.09 \).
However, the option "1 over 90" appears twice (once as option A and once as option D). Therefore, if you are selecting from these options and trying to match \( 0.09 \) via any of the given fractions, none of them is strictly correct. The closest fraction in terms of repeating decimals is "1 over 11," which results in a repeating pattern starting with the number 9 but isn't the same.
Final Conclusion: None of the listed options accurately represents the decimal \( 0.09 \).