# Order of Magnitude

by on July 27, 2009

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Although there are a number of variations for the term “order of magnitude”, the most widely used is that being a number rounded to the nearest power of 10. It allows scientists to have either a quick comparison of two or more related values or an idea of how large or small a single value is.

For example, Shaquille O’Neal has a height of 2.16 m (7’1″). In scientific notation, that can be expressed as 2.16 x 100 m. Thus, the order of magnitude of Shaq’s height is 100 m or 1 m. Of course, Shaq is much taller than just 1 m but his order of magnitude is within striking distance of 1 m than it is to the next order of magnitude which is 10 m.

Let’s have a much smaller example this time; say, an ant with a height of 8 x 10-4 meters. Now, some of you might be tempted to say that the order of magnitude of the ant is 10-4 meters. However, the correct answer is 10-3 meters. To elaborate, if you expand the given number: 0.0008, you can easily see that it’s nearer to 0.001 or 10-3 than it is to 0.0001 or 10-4.

At this point, we can now compare the heights of Shaq and the ant in terms of orders of magnitude. To do this, lets find out how many times larger is the Shaq’s order of magnitude to that of the ant’s. Hence, 100/10-3 = 103 or 1000. In other words, Shaq is 3 orders of magnitude taller than the ant.

Let’s bring in Kobe Bryant to help us give one last example. Kobe’s height is 1.98 m (6’6″) or 1.98 x 100 m; definitely much shorter than Shaq. However, as you can see, his height also has an order of magnitude equal to 100 m or 1 m. Hence, we can say that both basketball superstars have heights within the same order of magnitude.

Most science books express physical quantities in terms of orders of magnitude since it is sufficient to give the reader an idea how large or how small the object is. Like, it’s common to see the radius of the atom expressed as 10-10 m, the radius of the Earth as 107 m, the radius of the Sun as 109 m, and the distance of the Sun to Proxima Centauri (the nearest star to us aside from the Sun) as 1016 m.

We’ve got a few articles that touch on order of magnitude here in Universe Today. Here are two of them:

We also have Orders of Magnitude from NASA and a downloadable file from SLAC, Order-of-Magnitude Physics.

Tired eyes? Let your ears help you learn for a change. Here are some episodes from Astronomy Cast that just might suit your taste:

Source: Wikipedia

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