105 LearnersLast updated on June 9th, 2025
Decimal to Octal
The decimal number system (0 to 9) can be converted into an octal number system (0 to 7). This number system is used in the fields of electronics and computer science. In this article, we’ll be learning how decimal to octal conversion is done.
Decimal Number System Definition
This is the most commonly used number system. It forms the basis for mathematical calculations done in everyday life. It is also used to derive other numbering systems, including octal. Since it consists of 10 digits (0 to 9), the decimal number system is also called the base-10 number system.
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Octal Number System Definition
The octal number system has 8 digits (0 to 7). It is widely used in computing because binary numbers can be easily represented using the octal number system. Three binary digits correspond to one octal digit. Hence, conversions between octal and binary are easily achievable.
How to Convert Decimal to Octal?
To convert the decimal number system to octal, we have to divide the given number by 8. The division process continues until the quotient becomes 0. At the end, the remainders are written in the reverse order. Given below is a step-by-step explanation of the conversion.
Step 1: Write down the decimal number.
Step 2: For any decimal number less than 8, the octal equivalent will be the same.
- 010 = 08
- 110 = 18
- 210 = 28 and so on
- until 710 = 78
Step 3: If the given number is bigger than 7, then the number is divided by 8.
For example, to convert 156 to octal, let us start by dividing 156 by 8.
156 / 8 = 19 with 4 as the remainder.
Now divide the quotient (19) by 8.
19 / 8 = 2 with 3 as the remainder.
Once again, divide the quotient (2) by 8.
2 / 8 = 0 with 2 as the remainder.
Finally, write the remainder in reverse order to find the octal value equivalent of 156.
Therefore, 15610 = 2348
Decimal to Octal Conversion Table
A decimal to octal conversion table acts as a reference guide. It is used to determine the equivalent values of the decimal numbers in the octal number system. Given below is the decimal to octal conversion table.
Common Mistakes and How to Avoid Them in Decimal to Octal Conversion
It is quite common to make mistakes while converting decimal to octal number systems. So, it is important to get familiar with these mistakes to try and avoid them in the future. Here are a few common mistakes that we must watch out for when converting decimal to octal.
Mistake 1
Not Writing Remainders in Reverse Order
After dividing the given number by 8 until the quotient is 0, the remainder must be written down to get the final value. However, it is significant to write the remainders from bottom to top to get the conversion right.
Mistake 2
Dividing with Wrong Numbers
We must divide the number by 8 because octal is base-8. Dividing the number with any integer other than 8 will lead to wrong conversion.
Mistake 3
Stopping Too Early
The division process must continue until the quotient becomes 0. Failing to do so will result in errors.
Mistake 4
Not Cross Verifying
Students might not cross-verify their answer after the conversion. To avoid mistakes, it is always better to convert the result back to decimal to make sure the answer is correct.
Mistake 5
Confusing Quotient With Remainder
Students might get confused between quotient and remainder. To avoid this confusion, we must have a clear understanding of the two distinct concepts.
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Decimal to Octal Conversion Examples
Problem 1
How to convert 5⏨ to 5₈?
510 = 58
Explanation
Any decimal number less than 8 is the same as its octal equivalent.
Problem 2
A software engineer needs to convert 25 from decimal to octal for his new project. Help him convert the number.
318
Explanation
To convert 25 from decimal to octal, start by dividing 25 by 8.
25 / 8 = 3 with 1 as the remainder.
Now divide the quotient (3) by 8.
3 / 8 = 0 with 3 as the remainder.
Now that the quotient is 0, we can write down the remainders in the reverse order.
Hence, 2510 = 318
Problem 3
Add 15 and 50 and convert the sum into an octal number system.
1018
Explanation
First, let us add 15 and 50.
15 + 50 = 65.
Now, let us convert 65 from decimal to octal number system.
By dividing 65 by 8, we get 8 as the quotient and 1 as the remainder.
Now, by dividing the quotient (8) by 8, we get 1 as the quotient and 0 as the remainder.
Divide the new quotient (1) by 8 to get 0 as the quotient and 1 as the remainder.
Since we have 0 as the quotient, we can now write down the remainders in reverse order.
Therefore, 6510 = 1018
Problem 4
Convert 100 from decimal to octal
1448
Explanation
100 / 8 = 12 with 4 as the remainder.
Divide the quotient by 8. So 12 / 8 = 1 with 4 as the remainder.
Divide the new quotient by 8. 1 / 8 = 0 with 1 as the remainder.
Therefore, 10010 = 1448
Problem 5
An ethical hacker needs to convert the product of 20 and 10 from decimal to octal. Help him do it.
3108
Explanation
The product of 20 and 10 is 20 × 10 = 200.
Now convert 200 from decimal to octal.
200 / 8 = 25 and 0 is the remainder.
25 / 8 = 3 with 1 as the remainder.
3 / 8 = 0 and 3 is the remainder.
By writing the remainders in reverse order, we get 310.
Therefore, 20010 = 3108
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FAQs on Decimal to Octal
1.How many digits does the octal system have?
2.What is the difference between the decimal and octal number systems?
3.What is the relationship between octal and binary number systems?
4. Is it possible to convert decimal fractions to octal?
5. Is the octal number system important?
6.How can children in Philippines use numbers in everyday life to understand Decimal to Octal?
7.What are some fun ways kids in Philippines can practice Decimal to Octal with numbers?
8.What role do numbers and Decimal to Octal play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Decimal to Octal skills?
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Important Glossaries for Decimal to Octal Conversion
- Base-10: This refers to the decimal number system. It is called base-10 because every place value represents powers of 10. For example, 100, 101, 102, etc.
- Remainder: Remainder is the value that is left over after completing the division. While converting the decimal to an octal number system, the remainders are recorded and written from bottom to top to find the octal equivalent.
- Quotient: A quotient is the result that is obtained when a number is divided by another.
- Reverse order: In this article, reverse order refers to note down remainders from bottom to top. This is done to get the correct value of the conversion.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
