Scientific Notation

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The suspect is a male, age 1.73 × 109 s, height 1.83 m, weight 7.5 × 101 kg.

Big Ideas: 
  • How you express a numerical value determines your chance of being understood

"The suspect is a male, age 1.73 x 109 s, height 1.83 m, weight 7.5 x 101 kg."

Does this make any sense? Not much. The 1.83 m bit is the clearest, although 183 cm would be a more common expression for the height of a person. For the age and mass (commonly but incorrectly called "weight"), 55 years and 75 kg is much more comprehensible than 1.73 x 109 s and  7.5 x 101 kg.

"Scientific notation" is a style that we impose on students for some strange reason, but one that scientists avoid like the plague if at all possible, because it is so non-intuitive. Wherever we can, we use standard prefix notation: nm, μm, mm, m, km etc. Notice the values rise by factors of a thousand (or 103, if you insist). Now we can say that green light has a wavelength of 500 nm, which is more comprehensible, easier to remember, and requires less key strokes and awkward superscripts and symbols than 5.00 x 10-7 m.

The SI system of units (kg, m, s) is distinctly anthropocentric, but a lot of interesting stuff goes on at size scales that are vastly larger or smaller than we are. Thus, you would think that scientific notation would be most valuable in fields like in subatomic physics or cosmology. However, we still don't use scientific notation here either. We invent new non-SI units that allow us to write comprehensible numbers like 0.12 or 23.6, not 1,340,695,349 or 0.0000000001. Subatomic folks use the electron-volt (eV, keV, MeV, GeV etc.) and astronomers and cosmologists use the parsec (pc, kpc, Mpc  etc.).

So, if your granny asks you how far you ran in the half-marathon today, don't say "2.1 x 104 m". Say "21 km", even if she has a Ph.D in physics.

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