(12C) Decimal to Fraction

[Albert Chan]

(08-09-2018 11:13 AM)Thomas Klemm Wrote:  As we know \(\frac{113}{355}\) is closer for a long time. We have to wait until \(\frac{33215}{104348}\) to get closer

Hi, Thomas,

If you meant closer from below (i.e fraction < 1/Pi), above is correct.

However, if closer in absolute term, you don't have to wait that long.
For semiconvergent better than 113/355, solve for k

1/Pi - 113/355 = 2.703e-8 = (106 + 113k)/(333 + 355k) - 1/Pi
k ~ 145.8

If k >= 146, the fraction is closer.
For k = 146, we get 16604/52163, absolute error = 2.697e-8