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! :)

ConfuzzledKitten Jun 19, 2020

#1**+2 **

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

\(\dfrac1{b - 1} = 0.\overline{1}_b\)

MaxWong Jun 19, 2020

#2**+2 **

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!

ConfuzzledKitten
Jun 19, 2020

#4**+2 **

Thank you! I searched up a proof on Google and I think I understand now! :-)

ConfuzzledKitten Jun 19, 2020