B. Scale Factor

A scale factor is a ratio of two measurements. The first number represents a measurement on the diagram of the shape or object. The second number represents the corresponding measurement of the actual shape or object. Note that scale factors can be expressed in simplest fraction, decimal, or percent form.

The scale factor, k, is determined as follows:

where both measurements must be in the same units.

Example 1

The dimensions of a photo of a mountain bike rider are 15 cm by 9 cm.

An enlargement is to be made with poster-size dimensions of 4.0 m by 2.4 m.

Determine the scale factor, rounded to the nearest tenth.

Convert the dimensions of the photo from centimetres to metres.
15 cm = 0.15 m
9 cm = 0.09 m

Determine the scale factor for each measure. (It is always a good idea to confirm that the scale factor matches for each pair of corresponding dimensions.)

To the nearest tenth, the scale factor of the poster is 26.7.

Note that the scale factor in this case is larger than 1 because the photo has been enlarged. In other words, the dimensions of the poster are 26.7 times larger than the dimensions of the original photo.