Both scientists and engineers use proportionality and ratios to understand quantity and scale and the relationship between physical characteristics. To appreciate the relative magnitude of some properties or processes, it may be necessary to grasp the relationships among different types of quantities. For example, speed is the ratio of distance traveled to time taken and density is the ratio of mass to volume.

In thinking scientifically about systems and processes, it is essential to consider scale. Scientists study natural phenomena that span full scales of size, time, and energy, from very small to very large. Scientists can make macroscopic observations through direct observation with the naked eye. They use experimental techniques and tools to observe other scales that may be too small or large or too slow or fast to observe directly. 

A proper understanding of scale relationships is critical to engineering. A sense of scale is necessary to know what properties and aspects of shape or material are relevant at a particular magnitude or when investigating specific phenomena. Structures cannot be conceived or constructed without an engineer’s precise sense of scale.