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Octal to Decimal

Conversion of octal numbers to decimal is best done by the positional notation method. This process is the one we used to convert binary numbers to decimal.

First, determine the decimal equivalent for each position by multiplying 8 by itself the number of times indicated by the exponent. Set up a bar graph of the positions and values as shown below:

To convert an octal number to decimal, write out the number to be converted, placing each digit under the proper position.

Example:

Next, multiply the decimal equivalent by the corresponding digit of the octal number; then, add this column of figures for the final solution:

Solution: 743₈ is equal to 483₁₀

Now follow the conversion of 26525₈ to decimal:

Solution: 11,605₁₀ is the decimal equivalent of 26,525₈

To convert a fraction or a mixed number, simply use the same procedure.

Example: Change .5₈ to decimal:

Example: Convert 24.36₈ to decimal:

Solution: 24.36₈ equals 20.46875₁₀

If your prefer or find it easier, you may want to convert the octal number to binary and then to decimal.

Convert the following numbers to decimal:

Q.97 17₈.
Q.98 64₈.
Q.99 375₈ .
Q100. 0.4₈.
Q101. 0.61 ₈.
Q102. 10.22₈.