Decimal to Octal Converter — Free Online Tool
Enter a decimal fraction below to instantly convert it to its octal representation with a detailed step-by-step breakdown.
Octal Result
Step-by-Step Solution
Visual Representation
How to Convert Decimal Fractions to Octal
To convert a decimal number with a fractional part to octal, you split the number into its integer and fractional parts and convert them separately.
Steps
- Separate the number into the integer part and the fractional part.
- Convert the integer part to octal by repeatedly dividing by 8 and recording the remainders.
- Convert the fractional part to octal by repeatedly multiplying by 8 and recording the integer part of the result.
- Combine the two octal parts with a decimal point.
Example
Example: Try 255
Common Conversions
| Decimal | Octal |
|---|---|
| 0.125 | 0.1 |
| 0.25 | 0.2 |
| 0.5 | 0.4 |
| 0.75 | 0.6 |
| 1.5 | 1.4 |
Decimal to Binary
Convert decimal fractions to binary.
Decimal to Hexadecimal
Convert decimal fractions to hex.
Decimal to Fraction
Convert decimals to fractions.
Frequently Asked Questions
Common questions about octal conversion and base-8
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01 What is the octal numeral system?
Octal (base-8) uses digits 0 through 7. Each octal digit maps to exactly 3 binary bits, which made it convenient for early computing. For example, octal 75 = 7×8¹ + 5×8⁰ = 56 + 5 = 61 in decimal. Though less common today than hexadecimal, octal remains important in Unix/Linux file permissions.
02 How is octal used in Unix file permissions?
Unix/Linux file permissions use a 3-digit octal number like 755 or 644. Each octal digit encodes three permission bits: read (4), write (2), and execute (1). For example, 755 means the owner can read+write+execute (7 = 4+2+1), while group and others can read+execute (5 = 4+0+1). The command chmod 644 file.txt sets read+write for the owner and read-only for everyone else.
03 Why is octal less common today than hexadecimal?
Modern computer architectures are usually based on 16, 32, or 64 bits, which are more easily represented by base-16 (hex). Octal was more common with early 12-bit, 24-bit, or 36-bit systems.
04 How does base-8 relate to binary?
Every octal digit represents exactly 3 bits of binary data. For example, the octal digit 7 corresponds to the binary sequence 111.
05 Can decimal fractions easily be represented in octal?
A decimal fraction terminates in octal only if its denominator (in lowest terms) is a power of 8 (i.e., a power of 2). For example, 0.5 = 1/2 converts to 0.4 in octal (0.5 × 8 = 4.0). But 0.1 = 1/10 repeats in octal just as it does in binary, because 10 has a factor of 5.