while PI is _NOT_ 22/7... you do need an approximation that's useful from time to time.... so I proffer the following:
take the first 3 odd integers and write each twice: 11 33 55
break in the middle 113 355
divide in the (hopefully) obvious way: 355/113 for PI
that should be sufficiently accurate to within a foot/30cm/1 light nanosecond or so on the circumference of the earth
for a practical example, consider this: US Hat sizes are the diameter in 1/8ths of an inch.... all other hat sizes are circumferences in cms.... so what is the conversion factor.... I introduce a second approximation.... take the first two odd numbers and write each the number of times equal to the number...... so 1 333 split in the middle to get 13 inches = 33 cm
so the conversion factor for hat sizes is 355/113 * 33/13 or 11715 / 1469 or 7.97.....
so..... that's why we use 1/8th of an inch..... divide cms by 8 to get the US hat size diameter in inches (measured in 1/8ths).... and you can do it in your head... right there in the store :)