Question

doug measured a city park and made a scale drawing. the scale of the drawing was 6 centimeters = 2 meters. what is the drawings scale factor? simplify your answer and write it as a fraction.

Explanation:

Step1: Understand scale factor

Scale factor is drawing length over actual length. First, convert units to be the same. 2 meters = 200 centimeters.

Step2: Calculate scale factor

Drawing length is 6 cm, actual length is 200 cm. So scale factor is $\frac{6}{200}$. Simplify by dividing numerator and denominator by 2: $\frac{6\div2}{200\div2}=\frac{3}{100}$. Wait, no, wait. Wait, scale factor for drawing: wait, maybe I mixed up. Wait, scale is drawing : actual. Wait, the problem says 6 centimeters ≈ 2 meters. So drawing length is 6 cm, actual is 2 m = 200 cm. So scale factor (drawing to actual) is $\frac{6}{200}$? Wait no, maybe I got it wrong. Wait, scale factor is usually drawing length over actual length, but let's check. Wait, 6 cm on drawing represents 2 m (200 cm) in real. So the scale factor (drawing scale) is drawing length / actual length = 6 cm / 200 cm = 6/200 = 3/100? Wait no, maybe I messed up. Wait, no, scale factor for the drawing's scale: the scale is 6 cm : 2 m. Convert 2 m to cm: 2*100 = 200 cm. So the ratio is 6:200, simplify by dividing both by 2: 3:100. So as a fraction, drawing over actual is 6/200 = 3/100? Wait, no, maybe the other way? Wait, no, scale factor for the drawing (how much it's scaled down) is drawing length divided by actual length. So 6 cm represents 200 cm, so 6/200 = 3/100. Wait, but let's check again. 6 cm corresponds to 2 m (200 cm). So the scale factor is 6/200 = 3/100. Yes, that's correct.

Answer:

$\frac{3}{100}$