Express the following octal numbers into their equivalent decimal numbers:

(i) 145
(ii) 6760
(iii) 455
(iv) 10.75

Octal numbers can be converted to decimal by calculating the positional values for each digit. The conversions for the specified octal numbers are as follows: 145 = 101, 6760 = 3568, 455 = 301, and 10.75 = 8.953125 in decimal.
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Answered by Anonymous | 2025-07-04

To express octal numbers into their equivalent decimal numbers, you need to understand the concept of the octal and decimal numeral systems.
Octal to Decimal Conversion:
The octal numeral system is a base-8 system, which means it uses digits from 0 to 7. To convert an octal number to a decimal (base-10) number, each digit in the octal number is multiplied by 8 raised to the power of its position (counting from right to left, starting at 0).

Convert 145 to Decimal:

In octal, 14 5 8 ​ can be expanded as: 1 × 8 2 + 4 × 8 1 + 5 × 8 0 1 × 64 + 4 × 8 + 5 × 1 64 + 32 + 5 = 101
Therefore, the decimal equivalent is 10 1 10 ​ .


Convert 6760 to Decimal:

In octal, 676 0 8 ​ can be expanded as: 6 × 8 3 + 7 × 8 2 + 6 × 8 1 + 0 × 8 0 6 × 512 + 7 × 64 + 6 × 8 + 0 × 1 3072 + 448 + 48 + 0 = 3568
Therefore, the decimal equivalent is 356 8 10 ​ .


Convert 455 to Decimal:

In octal, 45 5 8 ​ can be expanded as: 4 × 8 2 + 5 × 8 1 + 5 × 8 0 4 × 64 + 5 × 8 + 5 × 1 256 + 40 + 5 = 301
Therefore, the decimal equivalent is 30 1 10 ​ .


Convert 10.75 to Decimal:

In octal, 10.7 5 8 ​ can be split into whole and fractional parts and expanded as:
Whole number: 1 × 8 1 + 0 × 8 0
Fractional part: 7 × 8 − 1 + 5 × 8 − 2
Calculating these parts:
Whole: 1 × 8 + 0 × 1 = 8
Fraction: 7 × 8 1 ​ + 5 × 64 1 ​
8 7 ​ = 0.875
64 5 ​ ≈ 0.078125
Sum: 8 + 0.875 + 0.078125 = 8.953125


Therefore, the decimal equivalent is approximately 8.95312 5 10 ​ .



By following this step-by-step method, you can convert any octal number into its decimal form accurately.

Answered by MasonWilliamTurner | 2025-07-06