Octal to decimal (floating point notation)

Question

I'm trying to convert this from Octal to Decimal, note that the 77 in octal and 8 is the base

(0.77 * 8^77) in octal = (0.984375 * 10^56) in decimal

but it's different from teacher's result:

7.72 * 10^56

Which one is correct?

Answer 1

The teacher's result comes from reading both the $77$'s as being in octal, though the $8$ as the base of the exponent should be written as $10_8$. In that case $$0.77_8=\frac {63}{64}$$ $$8^{(77_8)}=(8^{63})_{10}\\ \frac {63}{64} \cdot 8^{63} \approx 7.72 \cdot 10^{56}$$ It appears you have done $\frac {63}{64} \cdot 10^{56}$ but I don't know where you got $10^{56}$