To convert decimal to octal, we have to learn about both the number systems first. A number with base 8 is the octal number and a number with base 10 is the decimal number. Here we will convert a decimal number to an equivalent octal number. It is the same as converting any decimal number to binary or decimal to hexadecimal.

In decimal to binary, we divide the number by 2, in decimal to hexadecimal we divide the number by 16. In case of decimal to octal, we divide the number by 8 and write the remainders in the reverse order to get the equivalent octal number.

Decimal Number: All the numbers to the base ten are called decimal numbers. These are the commonly used numbers, which are 0-9. It has both integer part and the decimal part. It is separated by a decimal point (.). Numbers on the left of the decimal are integers and numbers on the right of the decimal is the decimal part. Example: (236.89)₁₀, (54.2)₁₀, etc.

Octal number: These are the numbers with base 8. If x is a number then the octal number is denoted as x₈. It contains digits from 0 to 7. Example: (212)₈, (121)₈, etc.

Convert Decimal to Octal with Steps

Follow the steps given below to learn the decimal to octal conversion:

1. Write the given decimal number
2. If the given decimal number is less than 8 the octal number is the same.
3. If the decimal number is greater than 7 then divide the number by 8.
4. Note the remainder, we get after division
5. Repeat step 3 and 4 with the quotient till it is less than 8
6. Now, write the remainders in reverse order (bottom to top)
7. The resultant is the equivalent octal number to the given decimal number.

For example: Convert 1792 into an octal number.

Also, read:

Decimal to Octal Table

Solved Examples

Example 1: Convert (127)₁₀ to Octal.

Solution: Divide 127 by 8

127 ÷ 8= 15(Quotient) and (7)Remainder

Divide 15 by 8 again.

15 ÷ 8 = 1(Quotient) and (7) Remainder

Divide 1 by 8, we get;

1 ÷ 8 = 0(Quotient) and (1) Remainder

Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number.

Hence, (127)₁₀ = (177)₈

Example 2: Convert 52₁₀ to octal.

Solution: Divide 52 by 8

52 ÷ 8 = 6(Quotient) and (4)Remainder

Divide 6 by 8 again.

6 ÷ 8 = 0(Quotient) and (6) Remainder

Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number.

Hence, (52)₁₀ = (64)₈

Example 3: Convert 100₁₀ to octal.

Solution: Divide 100 by 8

100 ÷ 8= 12(Quotient) and (4)Remainder

Divide 12 by 8 again.

12 ÷ 8 = 1(Quotient) and (4) Remainder

Divide 1 by 8, we get;

1 ÷ 8 = 0(Quotient) and (1) Remainder

Since the quotient is zero now, no more division can be done. So by taking the remainders in reverse order, we get the equivalent octal number.

Hence, (100)₁₀ = (144)₈

Practice Questions

1. Convert 456₁₀ to Octal  (Answer: 710₈)
2. Convert 212₁₀ to Octal   (Answer: 324₈)
3. Convert 101₁₀ to Octal  (Answer: 145₈)