Conversion from decimal to octal is very easy and simple if you understand it. However, I will try my best to make it simple for you. So, don’t worry.

As like as other conversion, here is also we will divide the entire conversion to two different categories. One is for integer part and other is for fraction part. I will discuss separately about both of them.

Now, lets see the rules for converting the integer portion first. Then we will see the rules for fraction portion to convert decimal to octal later in this post.

Table of Contents

## Decimal to octal number conversion

### Rules for integer number:

- Divide the decimal number by the base of octal number (8) and write the reminder.
- Divide the result again by 8 and write the reminder and continue this process until you get 0 at the result.
- Now write down the remainder in opposite order which will be the octal equivalent of given decimal number.

The following example will make you clear about these 3 rules for integer conversion. Let’s try to understand the given example.

**Example** : Convert (158)_{10} to equivalent octal number.

We have to convert the 10 based decimal number to its equivalent octal number which is 8 based. For this we can use any one method which are given bellow.

We have divided the number by the base of octal number and then taken the reminder in the given order indicated by the arrow.

For example, if we divide 158 by 8, then we will get the result 19 and reminder 6. If we divide 19 again by 8 then we will get 2 as the result and 3 as reminder. Just follow the process until you get zero at the result.

Now, try to convert some other numbers from decimal to octal using the same rules. This will help you to test yourself. So, practice yourself.

Take help from here if you can not solve anything properly. These rules were for only integer part. Now, we will see the rules for fraction number to convert decimal to octal.

### Rules for fraction number:

- Multiply the fraction part by 8 and write the integer portion.
- Again, multiply the resultant fraction part which you have got from the first process and write down the integer part and continue this process until you get zero at the fraction part (minimum 4 to 5 times if it repeats).
- Now write down the integers you have got at the same order you have got them.

You can also faced some difficulties to understand the above rules. However, I have discussed through an example conversion bellow. Just see this and feel how easy it is!

**Example** : Conversion of (.45)_{10} to equivalent octal number.

We will multiply the given number by the base of octal number and then write the integer part as the given direction by arrow.

Take the necessary digits after the decimal point although we have taken here from 5 digits after the radix point.

You can convert any fraction number from decimal to octal by the similar way. So, try this in your own.

I hope, you are now able to convert any decimal number to octal number after reading this post. If this is true, now try yourself to convert the following example from decimal to octal by your own.

I have given the solution for your learning purpose. Bus you should not see that solution before trying in your own. Now, try it.

**Example** : Conversion of (123.45)_{10} to octal number.

To convert the given decimal number to octal number we can use our previous concept. We will convert its integer and fraction part separately. At first we will convert the integer portion and then fraction part.

See the conversion of its integer part first.

Now, lets see the conversion of fraction portion of this given decimal number. The direction of arrow indicates the order of taking octal digits.

Now, we have got the total octal equivalent of this decimal number is (173.34631..)_{8} . Now, try to convert any other decimal number to its equivalent octal number using same method.

I think, you are now clear about this conversion from decimal to octal by reading this post. I have tried my best to make it very simple for you.

If you have any doubt for converting decimal to octal still now, then through it on the comment section bellow. We will try to solve your problem. Don’t forget to tell your experience about visiting our site.

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