Any decimal number can be converted to its octal equivalent.

For integers ,conversion is obtained just by dividing number continuously by 8 and keeping track of remainders obtained .

Example:

( 260 )₁₀= ( ? )8

Solution: Firstly Divide 260 by 8,
Now ,quotient obtained from this division will become dividend in next step,

dividend =32 ( rem=4 )
again, divide it with 2.( Keeping track of remainders),

dividend = 4 ( rem=0)

repeat the same process until dividend become less than the divisor.
now, dividend =4 is less than 8

Stop dividing when dividend become less than the divisor.

Now write in following sequence,
First write the last dividend in left and then write remainders obtained in reverse order .
As shown below,

(last dividend is 4 & remainders in reverse order)

So, the final answer is this , ( 4 0 4 )₈

While for fractional part ,the conversion is done by continuous multiplication by 8 and keeping track of the integers generated. See in given example,

Example:

( 0.625 )₁₀= ( ? )₈

Solution:

0.625 × 8 = 5.00 , integer obtained is 5

again, multiply the fractional part obtained with 8

0.00 × 8 = 0 ,integer obtained 0
now, we don’t have any fractional part left .So stop multiplying here.
Next step is , write down the integer obtained in the sequence they obtained after radix point ,as follows:

= ( 0.5 0 )₈=( 0.5 )8

This is the way we can convert a decimal number into its octal equivalent.

Another Example:

( 95.5 )₁₀= ( ? )₈Solution: Integer part:
divide 95 by 8 = 11 is obtained with rem 7
divide 11 by 8 = 1 is obtained with rem 3
now 1 < 8 so, 1 will be last dividend .Now write in reverse order 1 , 3 and then 7.

1 3 7

Fractional part:
0.5 × 8 = 4.00 , integer obtained is 4
now,multiply the fractional part obtained with 8 again,

.00 × 8 = 0 ,integer obtained 0.
now, we don’t have any fractional part left.
Answer:
= ( 1 3 7 . 4 0 )₈ = ( 1 3 7 . 4 )₈