Jerry made a scale drawing of a house. The scale of the drawing was 3 millimeters = 1 meter. What is the drawing's scale factor?

Question

Simplify your answer and write it as a ratio, using a colon.

Answer 1

To find the scale factor in a ratio format, we start with the given scale of the drawing: 3 millimeters = 1 meter.

First, we need to express both measurements in the same unit. Since 1 meter is equal to 1000 millimeters, we can convert the scale as follows:

3 millimeters = 1000 millimeters.

Now we have a ratio of 3 millimeters to 1000 millimeters. To simplify this ratio, we divide both sides by 3:

$$\frac{3}{3}:\frac{1000}{3}=1:\frac{1000}{3}.$$

Calculating $\frac{1000}{3}$:

$$\frac{1000}{3}\approx 333.33.$$

Since we need to express this accurately in ratio form, we can leave it as $\frac{1000}{3}$. The ratio then becomes:

1 : $\frac{1000}{3}$.

However, it's more common to express this in whole numbers. To achieve this, we can take the original ratio of 3:1000 and divide both sides by 3:

So we have: $$3:1000\to 1:\frac{1000}{3}\approx 1:333.33.$$

In terms of exact whole number representation, multiplying by 3 to avoid the decimal gives:

3 : 1000 = 3 : 1000.

Thus, the scale factor of the drawing is:

1 : 333.33 (or simply the ratio can remain presented as 3:1000 in whole numbers).

So we can say the simplified scale factor is:

1 : 333 (the simplest integer ratio).