Rationalizing Pi

Found an old Hemmi Mannheim type slide rule in the lab the
http://www.sphere.bc.ca/test/build.html [ slide rules ]
other day.

On the back was a series of settings to approximate the ratios
better than the eye and setting C1 or D1 to a number.

Linkname: pi is irrational
URL: http://www.lrz-muenchen.de/~hr/numb/pi-irr.html

Linkname: Math Forum - Ask Dr. Math
URL: http://mathforum.org/library/drmath/view/58725.html

Linkname: Pi -- from Wolfram MathWorld
URL: http://mathworld.wolfram.com/Pi.html

Linkname: Pi - Wikipedia, the free encyclopedia
URL: http://en.wikipedia.org/wiki/Pi

Interesting, for 3 figures, but for 2, mental is as good
and more interesting to the idea of Fermi question resolves.
Linkname: Fermi questions
URL: http://mathforum.org/workshops/sum96/interdisc/sheila1.html

Linkname: Fermi Questions / Fermi Problems
URL: http://www.vendian.org/envelope/dir0/fermi_questions.html

Some of the Hemmi slide rule conversion factors

Dia circle Circum
226 710
710 / 226
:= 3.14159292035398230088
vs. 3.141592653589793238462643383279502884 ...

from : http://www.geocities.com/SiliconValley/Pines/5945/facts.html

The fraction (22 / 7) is a well used number for Pi. It is accurate
to 0.04025%.
Another fraction used as an approximation to Pi is (355 / 113)
which is accurate to 0.00000849% [ same as the above 710/226 ]
A more accurate fraction of Pi is(104348 / 33215). This is accurate
to 0.00000001056%.

Other conversions were:
Side of sq diag of square
70 99

inches mm
5 127

feet metres
292 89

yards metres
35 32

miles km
87 140

...
cu ft imp gal
17 106

cu ft us gal
234 1750

cu ft litres
3 85
etc. etc.