2011/061) if x = 0.666... (base 8) and y = 0.555... (base 6), what is the value of y - x in base 7?

we need to compute x and y say in base 10

x = .6666 base 8
= (6/8)( 1 + (1/8)^2 + (1/8)^2 + ....
= (6/8) /(1-(1/8)) = (6/7)

y = .55555 (base 6) = 5/6( 1+ 1/6 + (1/6)^2 ....) = (5/6)/(1-1/6) = 1
hence
y - x = 1- 6/7 = 1/7 and hence .1 in base 7