Calculator
This tool converts positive, negative, whole, and fractional decimal numbers into octal notation.
Example Data Table
| Decimal | Octal | Notes |
|---|---|---|
| 8 | 10 | Smallest two-digit octal value from decimal input. |
| 25 | 31 | Shows repeated division by 8 for integers. |
| 64 | 100 | Exact octal power transition. |
| 156.375 | 234.3 | Includes both integer and fractional conversion. |
| -42 | -52 | Negative sign is preserved after conversion. |
Formula Used
Decimal to octal conversion uses repeated division for the integer part and repeated multiplication for the fractional part.
Integer part: Divide the decimal integer by 8 repeatedly. Record each remainder. Read the remainders from bottom to top.
Fractional part: Multiply the decimal fraction by 8 repeatedly. Record each whole-number digit in order.
General form: Octal = Σ(digit × 8position)
Check method: Convert the octal result back into decimal by summing each digit times its place value.
How to Use This Calculator
- Enter any decimal number, including optional fractional digits.
- Choose the fraction precision for the octal result.
- Enable detailed steps if you want to inspect each operation.
- Press Convert Now to display the answer above the form.
- Use the CSV or PDF buttons to save the result.
- Review the example table and formulas for validation.
Frequently Asked Questions
1. What does this calculator convert?
It converts decimal numbers into octal values. It supports whole numbers, negatives, and decimals with a selectable precision for the fractional part.
2. How is the integer part converted?
The integer part is divided by 8 repeatedly. Each remainder becomes an octal digit, and the digits are read in reverse order.
3. How are decimal fractions converted to octal?
The fractional part is multiplied by 8 repeatedly. The whole-number part from each multiplication becomes the next octal digit.
4. Why can some fractional results look long?
Some decimal fractions do not terminate neatly in base 8. The calculator stops at your chosen precision, so the result may be rounded by truncation.
5. Can I convert negative numbers?
Yes. The calculator converts the magnitude and then reapplies the negative sign to the final octal result.
6. What precision should I choose?
Use a small precision for quick answers and a larger precision when fractional accuracy matters. Eight digits works well for most learning tasks.
7. Can I export the result?
Yes. After conversion, you can download the current result as a CSV file or generate a simple PDF summary from the page.
8. Where is octal commonly used?
Octal appears in computing, digital systems, permissions notation, and number system education because it groups binary digits efficiently.