This number is not so much of a number as it is a notation, or a concept. It is understood as “the power of 10”, frequently called scientific notation. The engineer will consider this a wonderful number/notation/concept. It makes discussing and writing very, very large and very, very small numbers in a much easier manner.

So, say, you are in a discussion with a friend about the speed of light. You could say, “Well, the speed of light is known to be 299,792,458 meters per second, in a vacuum, of course.” But, that might lose people with that seemingly huge number, not to mention the time it takes to say that number. So, instead, round it off a bit, and say, “Well, the speed of light is known to be approximately 3.00 x 10^{8} meters per second, in a vacuum, of course.”

And, instead of saying, “Obviously, the wavelength of light emitted by a carbon dioxide laser is 0.0000106 meters,” you might want to say, “Obviously, the wavelength of light emitted by a carbon dioxide laser is 1.06 x 10^{-5 }meters.” Actually, when dealing with this, you probably would use the term, 10.6 micrometers, but, you get the idea.

Use the exponents of 10 and fit in with the crowd.