Octal To Decimal
1. We are given the octal number $(206, 104)_8$ and need to convert it to decimal.
2. Recall that in base 8 (octal), each digit represents a power of 8. Positions to the left of the decimal point have positive powers, and to the right have negative powers.
3. Separate the number into integer part $206_8$ and fractional part $104_8$.
4. Convert integer part $206_8$ to decimal:
$$206_8 = 2 \times 8^2 + 0 \times 8^1 + 6 \times 8^0 = 2 \times 64 + 0 + 6 = 128 + 6 = 134$$
5. Convert fractional part $0.104_8$ to decimal:
$$0.104_8 = 1 \times 8^{-1} + 0 \times 8^{-2} + 4 \times 8^{-3} = 1 \times \frac{1}{8} + 0 + 4 \times \frac{1}{512} = 0.125 + 0 + 0.0078125 = 0.1328125$$
6. Combine integer and fractional parts:
$$134 + 0.1328125 = 134.1328125$$
7. Therefore, the decimal equivalent of $(206, 104)_8$ is $134.1328125$.