How to calculate after decimal point of 99.21(Base 10) to (Base 8)?

Question

As I know by 0.21 x8 and -4 for the answer to convert to base 8.

However, I could not calculate and keep on expanding the value to millions.

Answer 1

$\frac18<0.21 <\frac28\\ 0.21-\frac18 = 0.085\\ 0.085*64 = 5.4\\ 0.085 - \frac5{64} = 0.006875\\ 0.006875 * 8^3 = 3.5\\ 0.006875 - \frac 3{8^3} = 0.00101625\\ $

etc.

$0.153$