To find an equivalent ratio to \( \frac{9}{78} \), we can simplify it by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 9 and 78 is 9.
Now, divide both the numerator and denominator by their GCD:
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} \quad (\text{rounded}) \]
However, let's check if \( \frac{9}{78} \) can match any of the given options without directly calculating the decimal.
- Trying \( \frac{3}{26} \): \[ 9 \div 3 = 3 \quad \text{and} \quad 78 \div 3 = 26 \] So, \( \frac{9}{78} = \frac{3}{26} \).
Since \( \frac{3}{26} \) simplifies to \( \frac{9}{78} \), the equivalent ratio is:
\[ \boxed{\frac{3}{26}} \]