If the base 8 decimal 0.30403...8 is equivalent to a/b, where a and b are relatively prime, express 2b - a in base 8.
What is this number? 0.30403...8
Do you mean that the number is repeating? Is the number 0.3040 where the 3040 keeps repeating?
And it is in base 8
If I have interpreted it correctly then
let
10000x = 3040.30403040... base 8
x = 0.30403040... base 8
7777x = 3040 base 8
\(x=\frac{3040}{7777}\;\;base8\\ x=\frac{340}{1111}\;\;base8\\ \)
a= 340 and b=1111
2b = 2222
a = 340
2b-a = 1662 (base 8)