Final answer:
To convert octal to decimal, multiply each digit by 8 raised to the power of its position. Octal 761 becomes 497 in decimal. The octal number 1276.445 becomes 702.572265625 in decimal.
Step-by-step explanation:
The process of converting octal numbers to decimal involves multiplying each digit by the power of 8 that corresponds to its position in the number, starting from the rightmost digit (which is the position for the power of 80). For example, the octal number 761 (a) can be converted to decimal by calculating (7 × 82) + (6 × 81) + (1 × 80) which equals 448 + 48 + 1, or 497 in decimal form.
For the octal number with a fractional part, such as 1276.445 (b), we extend this process to the fraction by using negative powers of 8 for the digits after the decimal point. Therefore, the conversion will involve (1 × 83) + (2 × 82) + (7 × 81) + (6 × 80) for the integer part, and (4 × 8-1) + (4 × 8-2) + (5 × 8-3) for the fractional part. The integer part equals 512 + 128 + 56 + 6 or 702 in decimal, and the fractional part is 0.5 + 0.0625 + 0.009765625 which sums up to 0.572265625. Therefore, when combined, the decimal equivalent of 1276.445 in octal is 702.572265625.