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}= ( ? )_{8}Solution:** 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}**

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