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At times, the world around us can be a difficult place to grasp. Three ways to help us make better sense of natural phenomena and engineered systems are scale, quantity, and proportion. You’ll learn about each of these in this lesson.

Size Is Relative

If you are trying to explain what a mouse is to someone who has never seen one, you might describe it as having big ears, a long tail, and fur all over its body. You might also give that person a sense of how small a mouse is by relating it to something they do know. For example, you might say that a mouse is smaller than an elephant’s toenail. Describing the mouse this way gives the person a really good sense of how small an animal it is, because you have described it in relation to something else. In other words, you gave it context.Many phenomena in our lives require context to really understand them.

Three ways that we can give things context are scale, quantity, and proportion.

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Scale gives us a way to understand relationships, and these relationships occur along continuums of size, time, and energy. In other words, things can be very large or very small (and everything in between). They can also happen in a very short period of time or a very long period of time. And, they can have very large or very small amounts of energy.

Without scale, we would have no reference for the size of the structures in these images.

SEM image with scale bar

For example, if we want to look at something very large, it doesn’t get bigger than the universe. It is so large, in fact, that it is difficult to comprehend. On the other end of the spectrum, we have atoms and subatomic particles such as protons and electrons, which are so small that you can’t even see them.

Mountain building happens on such a slow time scale that it does not even look like it is occurring.


In terms of time, we have processes such as mountain building, which takes so long and happens so slowly that it looks like it’s not happening at all. And in opposition to that we have light, which travels incredibly fast. Mountain building is also something that takes an enormous amount of energy, whereas something like the protons and electrons in an atom have a very small amount of energy.Scale helps us understand these natural phenomena, but it also helps us in engineering. Have you ever heard of a scale model? These are representations of real structures that are smaller in size and allow engineers to understand them and find solutions.

Scale models are miniature replicas of full-sized engineered structures.
scale model cars


Quantity allows us to understand ‘how much’ by using units of measure.

It is also important for these values to have context, which we get from the units and other information. For example, if you just say the value ‘1,000’, this doesn’t provide any useful information. One thousand what? Vultures? Grains of sand? Galaxies?And what is the context? If you have 1,000 grains of sand on the floor of your house, this will seem like a lot more sand than if you are at the beach, where 1,000 grains of sand is a drop in the bucket. But, if you have 10 people at the beach, this is a lot different than having 10 people at your house, where the space for them to fit in is smaller.

A gallon of water is a lot to you, but to the ocean it is insignificant.
ocean water

Units are especially important in engineering because the correct quantities are essential for functional systems. For example, if a beam should be 10 feet long, but someone else thinks it is supposed to be 10 meters long, then you’ve got a difference of about 22 feet! The quantities are very different and need to be described by their units to ensure accuracy.


Yet another way we can better understand natural and engineered phenomena is with proportion. Proportion is a ratio of one quantity to another, and allows us to better understand both scale and quantity. Proportion can describe two quantities that have the same units, or it can describe a relationship between quantities of different units.

Proportions like this one are ratios of two different quantities.
speed formula

For example, density is mass divided by volume, which can also be described as the quantity of mass to the quantity of volume. Another common proportion is speed, which is change in distance over change in time, or the quantity of distance to the quantity of time. And if you want to get your point across about how small a mouse is, just tell that person how many mice it would take to make up an entire elephant, or in other words, mice per elephant (it would be a lot for sure!).

Can you see how proportion, in addition to quantity and scale, can help us describe and understand the world around us, even the parts we can’t see?

Lesson Summary

Scale, quantity, and proportion are three different ways that we can look at our world with more context. This context helps us better understand not only natural phenomena but also engineered systems.Scale describes relationships along the continuums of space, time, and energy. How large or small is something? How fast or slow is the process? How much or how little energy is involved?Using units of measure, quantity describes how much of something we have. Even with units it can be helpful to put this value in context, such as the location or other descriptive factors.Proportion is a ratio between two different quantities, either of the same unit or of different units. It describes a relationship between the two quantities, like in mass, speed, and concentration, among other things.

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