To determine the scale factor used in Franco's drawing, we will set up a ratio of the dimensions of the drawing to the actual dimensions.
- Dimensions in the drawing: The width of the front lawn in the drawing is 3 millimeters.
- Actual dimensions: The actual width of the front lawn is 31 meters.
First, we need to convert the actual width from meters to millimeters since the drawing's dimensions are given in millimeters. We know that 1 meter is equal to 1000 millimeters. Therefore:
\[ 31 \text{ meters} = 31 \times 1000 \text{ millimeters} = 31000 \text{ millimeters} \]
Now we have:
- Width in the drawing: 3 mm
- Actual width: 31000 mm
Next, we find the scale factor by setting up the ratio of the dimensions:
\[ \text{Scale factor} = \frac{\text{Width in drawing}}{\text{Actual width}} = \frac{3 \text{ mm}}{31000 \text{ mm}} \]
Now, we simplify this fraction:
\[ \frac{3}{31000} \]
To simplify, we notice that both the numerator and the denominator can be divided by 1 (since 3 is a prime number and does not divide evenly into 31000). Thus, the fraction is already in its simplest form:
\[ \text{Scale factor} = \frac{3}{31000} \]
Therefore, the scale factor used in the drawing is
\[ \boxed{\frac{3}{31000}} \]