Some useful numbers

Prerequisite

Although our discussion of estimation suggests that you shouldn't memorize numbers in general, there are a few that are difficult to construct and that are very useful. I encourage you to learn these to the point that they seem sensible (so you don't mix up which is which).

Numbers related to your own body

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

 Inches Centimeters First joint of thumb Open handspan Forearm (cubit) Full height

Useful numbers from the world you live in

 Numbers 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 $2/π \times 10^7$ 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. Recently it was redefined in terms of directly measurable atomic properties.  But our stated result is correct to a couple of percent!

Joe Redish 7/13/11

Article 493