Question

Robert made a scale drawing of a petting zoo. The scale of the drawing was 8 millimeters = 4 meters. What is the drawing's scale factor?

Simplify your answer and write it as a fraction.

Answer 1

To find the scale factor, we start with the given scale of the drawing: \( 8 \) millimeters = \( 4 \) meters.

First, convert the meters to the same unit as the millimeters. Since \( 1 \) meter = \( 1000 \) millimeters, we convert \( 4 \) meters to millimeters:

\[
4 \text{ meters} = 4 \times 1000 \text{ mm} = 4000 \text{ mm}
\]

Now we can express the scale in terms of millimeters:

\[
8 \text{ mm} = 4000 \text{ mm}
\]

Next, we find the scale factor by simplifying the ratio of the drawing measurements to the actual measurements:

\[
\text{Scale Factor} = \frac{8 \text{ mm}}{4000 \text{ mm}} = \frac{8}{4000}
\]

Now we simplify the fraction \( \frac{8}{4000} \). We can divide both the numerator and the denominator by \( 8 \):

\[
\frac{8 \div 8}{4000 \div 8} = \frac{1}{500}
\]

Thus, the scale factor of the drawing is:

\[
\boxed{\frac{1}{500}}
\]