Final answer:
The correct scale factor for a dilation that produces a smaller figure is one that is less than 1, specifically B) One-third. This can be applied in proportions to find actual dimensions from scale measurements.
Step-by-step explanation:
When a dilation in mathematics results in a figure becoming smaller, we are looking for a scale factor less than 1. Among the options given, only one option is less than 1 and represents a scale that would produce a smaller figure. The correct choice is B) One-third. To apply this knowledge, we must set up proportions. For example, a proportion to find an actual dimension when given a scale dimension might look like this: 1/4 (scale factor) = 4 inches (scale dimension) : x inches (actual dimension).
Now, let's apply this to a real-world problem, such as determining the actual size of an object from a scale drawing. If a swimming pool has a diameter of 1(1/2) inches on the scale drawing with a scale factor of 1/72, the actual diameter can be found by the proportion 1/72 = 1.5 inches : x feet, which can then be solved to find the actual diameter.