The scale factor in a 1:200 drawing is represented as $\frac{1}{200}$ or $0.005$.

In a 1:200 scale drawing, each unit of measurement corresponds to 200 units of the same measurement in real life. For instance, $1$ centimeter on the drawing equates to $200$ centimeters (or $2$ meters) in reality. This scaling is particularly valuable in fields such as architecture and engineering, where large structures or areas need to be depicted on a more manageable scale.

To determine the scale factor, simply take the ratio provided (1:200) and express it as a fraction. In this case, $1:200$ translates to $\frac{1}{200}$, which evaluates to $0.005$. This fraction (or decimal) serves as the scale factor, indicating how much smaller the drawing is compared to the actual object.

Grasping scale factors is essential for accurately interpreting and creating scale drawings. To convert a measurement from the drawing to real life, you multiply the measurement on the drawing by the reciprocal of the scale factor (in this case, $200$). Conversely, to convert a real-life measurement to the drawing scale, you multiply by the scale factor ($0.005$).

For example, if a room measures $3$ centimeters in length on the drawing, its actual length would be calculated as:

On the other hand, if the actual room length is $10$ meters, it would be represented on the drawing as:

Comprehending these conversions ensures precision in both planning and interpreting scaled representations.