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0.816496580927726 as a fraction,if it's a rational or a irrational and also the steps or a guide on how to answer the problem.

 Oct 5, 2022
 #1
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+1

If you take its "continued fraction", you should get the following:

 

(0; 1, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 1, 2, 1, 2, 14, 2, 6, 2, 1, 8, 5, 1, 1, 1, 2, 1)

 

Converting the above to proper fractions, you get the following:

 

1
1 / 3
3 / 4
4 / 7
7 / 11
11 / 62
62 / 507
507 / 569
569 / 1645
1645 / 10439
10439 / 22523
22523 / 325761
325761 / 674045
674045 / 999806
999806 / 2673657
2673657 / 3673463
3673463 / 10020583
10020583 / 43755795
43755795 / 97532173
97532173 / 433884487
433884487 / 965301147
965301147 / 4295089075
4295089075 / 9555479297
9555479297 / 42517006263
42517006263 / 94589491823
94589491823 / 420874973555
420874973555 / 936339438933
936339438933 / 4166232729287
4166232729287 / 9268804897507
9268804897507 / 41241452319315
41241452319315 / 91751709536137
91751709536137 / 408248290463863


408248290463863 / 500000000000000

 

From the above, it appears to converge to a "rational fraction".

 

Note: The above was calculated by a computer programm in C++. If you don't understand "continued fractions", then you should consult your Math Teacher.
 

 Oct 6, 2022
 #2
avatar+14087 
+1

Hello Guest!

 

\(0.816496580927726\\ =\frac{816\ 496\ 580\ 927\ 726}{1\ 000\ 000\ 000\ 000\ 000} \color{blue}=\frac{4\ 082\ 482\ 900\ 463\ 863}{500\ 000\ 000\ 000\ 000}\ is\ a\ rational\ fraction.\)

laugh  !

 Oct 6, 2022
edited by asinus  Oct 7, 2022

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