Did I Invent This (REALLY Nerdy Content)

[sthief09]

or is it already invented?

for figuring out decimals for fractions with denominator 7. take the numerator, double it, multiply by 7. then divide by 100. add that to the numerator doubled twice, multiplied by 7, and divided by 100 twice.

take 1/7 for example. 1*2*7/100 = .14. add 1*2*2*7/100/100 = .0028. add 1*2*2*2*7/100/100/100 = .000056. sum that and you get .142845. keep going and it keeps expanding. it works for all 7's. divide all that by 2 and it works for the 14 demoninators. it's pretty useful for quick approximations. you just double ti and append, double it and append, double it and append. once the doubles start getting into triple digits, it starts having a big impact. but for most, it works well for the first 6 digits. for 2/7 it's just .2856 + .000108 so .285708, which you can round to .28571

in series form, it's the sum from n= 1 to fininity of numerator*7*(2^n)/100^n

I'm assuming that the series boils down to numerator/7. does anyone know if someone's already done this?