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Decimal to Octal

Here we are going to learn how to convert decimal to octal. Octal number is a number to the base 8 and decimal number is the number to the base 10. Here we will learn how to convert an decimal number to an equivalent octal number. It is similar to converting decimal to binary or decimal to hexadecimal. In decimal to binary we divide with 2, in decimal to hexadecimal we divide with 16 and here we divide the given decimal number with 8 and write the remainders in the reverse order to get the equivalent octal number.

Decimal number:

Set of all Number to the base ten is called as decimal numbers.It contains numbers from 0-9. This is commonly used number system. It has integer part and decimal part. It is separated by decimal point number on left of decimal point is integer part and numbers on right of decimal point is decimal part.

Example: (1) 52.3 (2) 45 (3) 698.51

Octal number:

Octal numbers are numbers with base 8. If a is a number then the octal number is denoted as a8. It contains digits from 0 to 7. It is not widely used.

Example: (1) 125 (2) 675 (3) 471

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How to Convert Decimal to Octal

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Below are the steps on decimal to octal conversion -

Step 1: Take the given decimal number

Step 2: If the number is less than 8 the octal number is the same

Step 3: If the number is greater than 7 then Divide the number with 8

Step 4: Note the remainder

Step 5: Carry on the step 3 and 4 with the qoutient till it is less than 8

Step 6: Write the remainders in reverse order(bottom to top)

Step 7: The resultant is the equivalent octal number to the given decimal number

Decimal to Octal Conversion

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Below are the examples on converting decimal to octal -

Solved Examples

Question 1: Convert 128 to octal form.
Solution:
Given decimal number is 128

Start the division process

8 | 128
8 | 16 -- 0
8 | 2 -- 0
8 | 0 --2



Correct answer is The equivalent octal number for 128 is 2008
Question 2: Convert 58 to octal form
Solution:
Given decimal number is 58

Start the division process

8 | 58

8 | 7 -- 2

8 | 0 --7



Correct answer is the equivalent octal number for 58 is 728
Question 3: Convert 451 to octal form
Solution:

Given decimal number is 451

Start the division process

8 | 451

8 | 56 -- 3

8 | 7 -- 0

8 | 0 -- 7



Correct answer is the equivalent octal number for 128 is 7038
Question 4: Convert 4 to octal form?
Solution:
Given decimal number is 4

Since 4 is less than 7

Correct answer is the equivalent octal number for 4 is 48
Question 5: Convert 287 to octal form.
Solution:
Given decimal number is 287

Start the division process

8 | 287
8 | 35 -- 7
8 | 4 -- 3
8 | 0 --4


Correct answer is the equivalent octal number for 287 is 4378
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