There are a number of ways that measurement is connected to ratio and proportion:
1. Scale drawings use a scale factor (the ratio of the actual length to the scale length) to transform diagrams into usable sizes. For instance, architectural drawings for a building are drawn on paper that fits on a table. Models are drawn or produced on a scale where the proportion of corresponding lengths is the constant.
2. We use proportions when modifying a recipe for the number of servings to prepare. If the recipe says it will serve 4 people, but 6 people are in attendance, we scale the recipe up by a factor of 3/2. Thus, each measure of ingredients is also scaled up by 3/2.
3. Many medical measurements are proportions: BAC (blood alcohol content) is the amount of alcohol present in a blood sample, represented as a percent; oxygen levels in the bloodstream are given as a percent; doctors consider the ratio of "good" cholesterol to "bad" cholesterol.
4. When measuring a student's performance, we often mark the ratio of correct items to total items tested.
5. When translating from one measurement system to another, we rely on proportions. For example, 1 inch is equivalent to 2.54 centimeters. With this, we can convert lengths given in inches or feet to centimeters (and ultimately meters).
There are countless other examples. The concept of ratio and proportion, combined with basic measurements, allows us to measure things by inference—for instance, we know how large stars are, despite the fact that we have only managed to send craft to one star (the sun). We use proportions to give estimates for the size and mass of these objects.