Class Content I >Modeling with mathematics > Using math in science > Dimensions and units > Estimation
2.1.4.3
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.
Numbers


Number of people on the earth

~8 billion (8 x 10^{9})

Number of people in the USA

~ 300 million (3 x 10^{8})

Number of people in the state of Maryland

~ 5 million (5 x 10^{6})

Number of students in a large state university

~3040 thousand (3 x 10^{4})

Macro Distances


Circumference of the earth

~24,000 miles (1000 miles/time zone at the equator) 
Radius of the earth*

2/π x 10^{7} m

Distance across the USA 
~3000 miles

Distance across DC

~10 miles

Micro Distances


Size of a typical animal cell

~1020 microns (10^{5} m)

Size of a bacterium, chloroplast, or mitochondrion

~1 micron (10^{6} m)

Size of a mediumsized virus

~0.1 micron (10^{7} m)

Thickness of a cell membrane

~510 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  but the stated result is correct to a couple of percent!
Joe Redish 7/13/11
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