Physics Topics: Length Scales, Orders of Magnitude, and Scientific Notation

During the first week or so of your physics class, your teacher will most likely talk about the various length scales present in the universe.  These length scales range from very small elementary particles such as electrons, protons, and neutrons with widths of ~5x10-15 meters, to the width of our very own galaxy the Milky Way of ~1.2x1021 meters.  Physicists study all of these length scales, with quantum mechanics studying physical phenomena at microscopic scales, and astrophysics studying the very large objects scattered throughout the universe.  When scientists talk about orders of magnitude, what they are really referring to is the relative difference between two numbers in their power of ten.  For instance, the difference in the power of ten between the width of an elementary particle and the width of the Milky Way is 36 (21-(-15)=36), so we say that these length scales are separated by 36 orders of magnitude. Physics truly studies all physical length scales in the universe!  Rather than writing these very large or very small numbers out fully with a lot of zeros before or after the decimal place, it is often easier to write them in scientific notation as I have done above.  You will inevitably encounter scientific notation in your physics and chemistry classes.  While scientific notation may seem difficult to use at first, learning it well will ultimately be an advantage to you throughout the rest of the semester.

A diagram of the various length scales in the universe.  You can click on each object to learn more about it.  http://htwins.net/scale2/

Scientific notation: http://en.wikipedia.org/wiki/Scientific_notation

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