Question

Convert from octal to decimal:
a. 761
b. 1276.445

Answer 1

To convert octal to decimal, multiply each digit by 8 raised to the power of its position. Example 761 in octal is 497 in decimal and 1276.445 in octal is approximately 702.57227 in decimal. Scientific notation for these would be 4.97×10² and 7.0257227×10², respectively.

Step-by-step explanation:

To convert from octal to decimal, you need to understand that octal is a base-8 number system. This means that each digit represents a power of 8. To convert an octal number to decimal, you'll multiply each digit by 8 raised to the power of its position, counting from right to left starting at 0. Let's look at the examples you provided:

1. 761 in octal:
   7×58² + 6×58¹ + 1×58° = 7×64 + 6×58 + 1 = 448 + 48 + 1 = 497 in decimal.
2. 1276.445 in octal:
   For the whole number part: 1×58³ + 2×58² + 7×58¹ + 6×58° = 1×512 + 2×64 + 7×58 + 6 = 512 + 128 + 56 + 6 = 702 in decimal.
   For the fractional part, we'll multiply each digit by 8 raised to the power of its negative position: 4×58⁻¹ + 4×58⁻² + 5×58⁻³ = 4/8 + 4/64 + 5/512 = 0.5 + 0.0625 + 0.00977 = 0.57227 (approx).
   Combining the whole with the fractional part, you get 702.57227 in decimal.

To express these numbers in scientific notation:

1. 497 in decimal is written as 4.97×10².
2. The decimal 702.57227 approximated would be 7.0257227×10².