Question

Grace measured a city park and made a scale drawing. The scale she used was 9 centimeters = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a ratio, using a colon.

Answer 1

To express the scale of 9 centimeters = 1 meter as a scale factor, we can represent it as a ratio.

First, we note that 1 meter is equal to 100 centimeters. Therefore, we can convert the scale into centimeters:

Scale: 9 centimeters (drawing) = 100 centimeters (actual size).

Now, we can write this as a ratio:

\[
9 \text{ cm} : 100 \text{ cm}
\]

To simplify this ratio, we divide both sides by 9:

\[
1 : \frac{100}{9}
\]

Expressing \( \frac{100}{9} \) as a decimal gives approximately 11.11, but we generally keep the ratio in fractional form. Therefore, the final answer is:

\[
1 : \frac{100}{9}
\]

Alternatively, if we want to express it in a simpler integer format:

The simplified form of the ratio is:

\[
9 : 100
\]

So the scale factor of the drawing is:

\[
\boxed{9:100}
\]