To find the scale factor of the drawing, we begin with the scale provided: 6 centimeters = 9 meters.
We can express this as a fraction:
\[ \text{Scale Factor} = \frac{\text{Length in drawing (cm)}}{\text{Actual Length (m)}} \]
Substituting the values gives us:
\[ \text{Scale Factor} = \frac{6 \text{ cm}}{9 \text{ m}} \]
To simplify this fraction, we need to convert the meters to centimeters since we're comparing lengths in the same units. We know that 1 meter = 100 centimeters, so:
\[ 9 \text{ m} = 9 \times 100 \text{ cm} = 900 \text{ cm} \]
Now, we can substitute this back into our scale factor:
\[ \text{Scale Factor} = \frac{6 \text{ cm}}{900 \text{ cm}} \]
This fraction can be simplified by dividing both the numerator and the denominator by 6:
\[ \text{Scale Factor} = \frac{6 \div 6}{900 \div 6} = \frac{1}{150} \]
Thus, the simplified scale factor of the drawing is:
\[ \boxed{\frac{1}{150}} \]