Find the decimal equivalent of octal number 127.548 :

To convert a number from octal (base 8) to decimal (base 10), expand it using positional place values: each digit is multiplied by 8 raised to the power of its position, counted outward from the radix point — positive powers 80, 81, 82 … for the integer digits (right to left), and negative powers 8-1, 8-2 … for the fractional digits (left to right). Summing all the products gives the decimal value.

1. Write the integer part 1278 using place values: 1×82 + 2×81 + 7×80.

2. Evaluate: 1×64 + 2×8 + 7×1 = 64 + 16 + 7 = 87.

3. Write the fractional part .548 using place values: 5×8-1 + 4×8-2.

4. Evaluate: 5×(1/8) + 4×(1/64) = 0.625 + 0.0625 = 0.6875.

5. Combine the two parts: 87 + 0.6875 = 87.687510.

Cross-check via binary: since 8 = 23, each octal digit expands to exactly 3 binary bits (1→001, 2→010, 7→111, 5→101, 4→100), giving 001010111.1011002. Evaluating this binary value independently: the integer part 10101112 = 64+16+4+2+1 = 87, and the fractional part .1011002 = 0.5+0.125+0.0625 = 0.6875 — the same result, confirming the answer.

So the decimal equivalent of 127.548 is 87.687510.