Orders of Magnitude

Science deals with both very large and very small numbers.  This video was made in 1977 by Charles and Ray Eames for IBM.  It is a fantastic voyage through the very large and small sizes of the components of our Universe.





DEFINE - The order of magnitude of a number is the power of 10 that is closest to the numerical value of a measurement or quantity.  


Scientific notation is how scientists write large and small numbers in an efficient manner that easily indicates the order of magnitude of the value.  A change of one order of magnitude is the same as multiplying or dividing a number by 10.  For example 3452 is one order of magnitude larger than 345.2 and two orders of magnitude larger than 34.52. 




USE - Orders of magnitude are very useful for rough estimations and they also give us a very quick indication of the difference between two quantities.  For example Einstein's mass might have been about 75 kg.   The nearest power of 10 to his mass would be 102 or 100 kg.  For comparison, the average mass of a mouse is about 0.035 kg (35 g) which is closest to 10-2 kg and a male African elephant would be close to 104 kg (here we are not saying the mass of the elephant is 10 000 kg - no elephant is that big - but rather the elephant's mass is much closer to 10 000 kg than it is to 1000 kg).


Having trouble understanding exponents.  Watch this quick video.  Half the story is missing though, can you determine what other example this video should have included?


APPLY - By looking at the exponent value of the nearest power of ten, we can make simple order of magnitude comparisons.  Einstein's mass is 4 orders of magnitude (2 minus -2) or about 104 times more than that of the mouse.  Compare the mass of the elephant to that of the mouse (see below for the correct response). 


Order of magnitude becomes very important when we consider the range of measurements possible in our physical world.  Here are some quantities in our Universe expressed to the nearest power of 10.  Compare the radius of our solar system to the radius of an atom.



More information, an alternate explanation, and the source of this table can be found here.


ANSWERS - The elephant (104 kg) has a mass 6 orders of magnitude (106, a million times) greater than the mouse (10-2 kg).  The radius of an atom is 1023 times (that is a 1 with 23 zeros) smaller than the solar system.




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