+55 For each part of this problem, convert the fraction to a "decimal" in the specified base.
(a) Convert the fraction 1/2 to base 3
(b) Convert the fraction 1/7 to base 8
(c) Convert the fraction 1/(b-1) to base b
Thank you in advance! :)
+9673 Because \(\dfrac13 + \dfrac1{3^2} + \dfrac1{3^3} + \cdots = \dfrac{\dfrac13}{1 - \dfrac13} = \dfrac12\),
\(\dfrac12 = 0.\overline{1}_3\)
By a similar approach,
\(\dfrac17 = 0.\overline{1}_8\)
and
\(\dfrac1{b - 1} = 0.\overline{1}_b\)
+55 Thank you for replying! I do not really know how you got the first equation, I might be missing something really simple, but if you have the time, could you explain it to me? Thanks!
+55 Thank you! I searched up a proof on Google and I think I understand now! :-)
