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Useful numbers (2013) (redirected from Useful numbers (2015))

Page history last edited by Mark Eichenlaub 5 years, 6 months ago Saved with comment

Class Content I >Modeling with mathematics > Using math in science Dimensions and units > Estimation


When doing estimation problems, most of the time, the best approach is to start with something you know and can quantify.  But there there will be times when that would take too long or be too uncertain. In those cases, it's useful to have a few numbers that you have learned and that you can use as a reference point. 


Take these measurements and remember them so you can use them to use as measuring sticks in your estimations:

  • the first joint of your thumb,
  • your handspan,
  • the length of your forearm, and
  • your height (preferably in cm) 


Here are a few useful numbers to keep in mind.


Number of people on the earth
~8 billion (8 x 109)
Number of people in the USA
~ 300 million (3 x 108)
Number of people in the state of Maryland
~ 5 million (5 x 106)
Number of students in a large state university
~30-40 thousand (3 x 104)
Macro Distances
Circumference of the earth
~24,000 miles (1000 miles/time zone at the equator)
Radius of the earth*
2/π x 107 m
Distance across the USA ~3000 miles
Distance across DC
~10 miles
Micro Distances
Size of a typical animal cell
~10-20 microns (10-5 m)
Size of a bacterium, chloroplast, or mitochondrion
~1 micron (10-6 m)
Size of a medium-sized virus
~0.1 micron (10-7 m)
Thickness of a cell membrane
~5-10 nm (10-8 m)
Radius of an atom ~ 0.1 nm ( 10-10 m)


* This interesting relation -- that the radius of the earth is 2/π times 107 meters -- is not an accident. When the meter was first defined during the French Revolution, it was defined so that the distance from the north pole to the equator along the longitude running through Paris was exactly 10,000 km.  This makes the circumference of the earth 40,000 km. Setting this = 2πR gives the indicated result.  Of course, this was too hard to measure exactly, so it was redefined to be a particular distance between two scratches on a carefully controlled metal bar -- but the stated result is correct to a couple of percent!


Joe Redish 7/13/11

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