Decimal to Octal

Here's how the conversion works:

Integer Part Conversion:

• Divide the decimal number by 8.
• Record the remainder, which represents the least significant octal digit (LSO).
• Repeat the division process with the quotient until it becomes zero.
• The octal equivalent is obtained by reading the remainders in reverse order..

Fractional Part Conversion (if applicable):

• Multiply the fractional part by 8
• Record the integer part of the result, which represents the next digit after the decimal point.
• Repeat the multiplication process with the fractional part until it becomes zero or until the desired precision is reached.

Example Conversion:

Convert the decimal number 1234.567 to octal

Integer Part Conversion:

• Dividing 1234 by 8, we get quotient 154 and remainder 2.
• Dividing 154 by 8, we get quotient 19 and the remainder 2.
• Dividing 19 by 8, we get quotient 2 and remainder 3.
• Dividing 2 by 8, we get quotient 0 and remainder 2.

Reading the remainders in reverse order: 2322.

Fractional Part Conversion:

• Multiplying 0.567 by 8, we get 4.536. The integer part is 4.
• Multiplying 0.536 by 8, we get 4.288. The integer part is 4.
• Multiplying 0.288 by 8, we get 2.304. The integer part is 2.
• Multiplying 0.304 by 8, we get 2.432. The integer part is 2.
• Multiplying 0.432 by 8, we get 3.456. The integer part is 3.
• Multiplying 0.456 by 8, we get 3.648. The integer part is 3.
• Multiplying 0.648 by 8, we get 5.184. The integer part is 5.
• Multiplying 0.184 by 8, we get 1.472. The integer part is 1.
• Multiplying 0.472 by 8, we get 3.776. The integer part is 3.
• Multiplying 0.776 by 8, we get 6.208. The integer part is 6.
• Multiplying 0.208 by 8, we get 1.664. The integer part is 1.
• Multiplying 0.664 by 8, we get 5.312. The integer part is 5.
• Multiplying 0.312 by 8, we get 2.496. The integer part is 2.
• Reading the integers in order: 0.4422335136152

Octal Equivalent:

Combining the integer and fractional parts, we get:

• Integer part: 2322
• Fractional part: .4422335136152
• Octal equivalent: 2322.4422335136152

The decimal number 1234.567 is equivalent to 2322.4422335136152 in octal notation.