How to Convert Decimal to Octal Using Division Method with Solved Examples
The concept of Convert Decimal to Octal plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding decimal to octal conversion helps students work with different number systems, especially in computer science and digital electronics.
What Is Convert Decimal to Octal?
Convert Decimal to Octal means changing a number from decimal (base-10) format to octal (base-8) format. In mathematics and computer science, this concept is crucial for understanding how numbers are represented and used by digital systems, such as computers and microcontrollers. You'll also find decimal to octal conversion applied in areas like computer programming, error coding, and data encoding.
Key Formula for Convert Decimal to Octal
Here’s the standard method:
For the integer part: Successively divide the decimal number by 8 and write down the remainder each time until you reach zero. The octal number is the string of remainders read from last to first.
For the fractional part: Multiply the decimal fraction by 8, take the integer part as the next octal digit, and repeat with the fraction that remains.
How to Convert Decimal to Octal?
To convert a decimal number to octal, follow these clear steps:
- Divide the integer part of the decimal number by 8.
- Record the remainder.
- Use the quotient and repeat the process (divide by 8 again) until the quotient is zero.
- Write the sequence of remainders in reverse order—this is the octal equivalent of the integer part.
- If there is a fractional part, multiply it by 8.
- The whole number part of the result is the next octal digit after the decimal point.
- Repeat the process with the new fractional part as needed.
Step-by-Step Illustration
Example 1: Convert 45 (decimal) to octal.
2. 5 ÷ 8 = 0 remainder 5
3. Collect the remainders in reverse: 55
So, 45 in decimal = 55 in octal.
Example 2: Convert 789.625 (decimal) to octal.
1. 789 ÷ 8 = 98 remainder 5
2. 98 ÷ 8 = 12 remainder 2
3. 12 ÷ 8 = 1 remainder 4
4. 1 ÷ 8 = 0 remainder 1
Remainders (reverse order): 1, 4, 2, 5 → 1425 (octal integer part)
Fractional part (.625):
1. 0.625 × 8 = 5.0 → whole part: 5, fraction: 0.0
Thus, the octal fraction is .5
Final octal: 1425.5
Conversion Table: Decimal to Octal (0–20)
| Decimal (Base 10) | Octal (Base 8) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |
| 16 | 20 |
| 17 | 21 |
| 18 | 22 |
| 19 | 23 |
| 20 | 24 |
Rules, Tips & Tricks
- For decimal to octal, always use division by 8 for the integer part and multiplication by 8 for the fraction.
- The octal number system has only digits from 0 to 7. If your answer has 8 or 9, double-check your steps.
- Write down remainders carefully and always reverse their order for the final answer.
- For fractions, decide how many octal digits you want after the point and stop when you have them or if the fraction turns zero.
- Zero-padding at the left does not change the octal value; 007 is the same as 7 in octal.
Calculator and Online Tools
You can convert decimal to octal quickly using online calculators or by coding. For example, here’s a simple method in Python:
# Python code to convert decimal to octal decimal_num = 789 octal_num = oct(decimal_num) print(octal_num) # Output: 0o1425
Such tools are helpful during exams or assignments for instant conversion. Vedantu’s online maths resources often include calculators and number system converters to boost your preparation.
Convert Decimal to Octal in Real Life
Decimal to octal conversion is not only for school exams. It is widely used in computers to represent file permissions (like in Linux), microcontroller coding, and digital circuit design. Understanding this helps in fields from information technology to electronics engineering.
Try These Yourself
- Convert 210 (decimal) to octal.
- Change 673.23 (decimal) to octal (round to 2 octal digits after the point).
- What is the octal of 128?
- Give the octal for 0.375 in decimal.
- Check if 60 decimal is 74 octal.
Frequent Errors and Misunderstandings
- Confusing the algorithm with decimal–to–binary (divide by 2) or decimal–to–hex (divide by 16).
- Forgetting to reverse the remainder order for the final octal number.
- Using 8 or 9 in octal digits—octal only uses 0 to 7.
- Stopping fractional conversion too early or not rounding as required.
Relation to Other Concepts
The idea of convert decimal to octal connects closely with decimal to binary conversion and hexadecimal number system in both maths and computer science. It is also related to understanding bases, which makes future concepts in data encoding and digital logic much easier.
Classroom Tip
A quick way to remember decimal to octal conversion: "Divide integers, multiply fractions by 8, and always write remainders or integer parts in reverse." Vedantu’s teachers use stories and visual tables for memorable pattern recognition in live classes.
We explored convert decimal to octal—from what it means to key steps and real examples, common mistakes, real-life uses, and related topics. With regular practice and Vedantu’s maths support, you’ll solve all number system conversions with confidence!
For more about number systems, explore these helpful resources:
FAQs on Convert Decimal to Octal Number System
1. What is the method to convert decimal to octal?
The method to convert decimal to octal is to repeatedly divide the decimal number by 8 and write down the remainders until the quotient becomes 0.
- Step 1: Divide the decimal number by 8.
- Step 2: Record the remainder.
- Step 3: Divide the quotient again by 8.
- Step 4: Repeat until the quotient is 0.
- Step 5: Write the remainders in reverse order to get the octal number.
2. How do you convert 100 from decimal to octal?
The decimal number 100 is equal to 144 in octal.
- 100 ÷ 8 = 12, remainder 4
- 12 ÷ 8 = 1, remainder 4
- 1 ÷ 8 = 0, remainder 1
3. What is the formula for converting decimal to octal?
There is no single algebraic formula, but the conversion is based on repeated division by base 8.
- Decimal number = (Quotient × 8) + Remainder
- Repeat division until quotient = 0
- Octal number = remainders written in reverse order
4. How do you convert a decimal number with fractions to octal?
To convert a decimal fraction to octal, multiply the fractional part repeatedly by 8 and record the integer parts.
- Step 1: Separate integer and fractional parts.
- Step 2: Convert integer part using division by 8.
- Step 3: Multiply fractional part by 8.
- Step 4: Record the integer part each time.
- Step 5: Repeat until fraction becomes 0 or reaches desired precision.
5. Why do we divide by 8 when converting decimal to octal?
We divide by 8 because the octal number system is a base-8 system.
- Each digit in octal represents powers of 8.
- Division by 8 extracts the least significant digit first.
- Repeated division builds the full octal representation.
6. What are the digits used in the octal number system?
The octal number system uses digits from 0 to 7 only.
- Valid digits: 0, 1, 2, 3, 4, 5, 6, 7
- Digits 8 and 9 are not allowed in octal.
7. Can you give another example of converting decimal to octal?
Yes, the decimal number 83 converts to 123 in octal.
- 83 ÷ 8 = 10, remainder 3
- 10 ÷ 8 = 1, remainder 2
- 1 ÷ 8 = 0, remainder 1
8. What is the difference between decimal and octal number systems?
The main difference is that decimal is a base-10 system while octal is a base-8 system.
- Decimal uses digits 0–9.
- Octal uses digits 0–7.
- Decimal place values are powers of 10.
- Octal place values are powers of 8.
9. What are common mistakes when converting decimal to octal?
A common mistake in decimal to octal conversion is forgetting to write the remainders in reverse order.
- Not reversing the remainders.
- Using 10 instead of 8 as the divisor.
- Including digits 8 or 9 in the final octal answer.
10. Where is decimal to octal conversion used in real life?
Decimal to octal conversion is mainly used in computer science and digital electronics.
- Representing binary numbers in compact form.
- File permission systems in Unix/Linux (e.g., 755).
- Low-level programming and machine code.
