(12C) Decimal to Fraction
08-11-2018, 02:13 AM
Post: #44
 Albert Chan Senior Member Posts: 1,998 Joined: Jul 2018
RE: (12C) Decimal to Fraction
(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
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