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Table of Contents

Decimal system for the general public is the most familiar number system among binary, octal, and hexadecimal number system. Base 10 has 10 symbols only: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Whereas the octal system represents 7 numbers as one of the numbers systems. So, base 8 has only eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7.

There are different methods of converting decimal to octal, either direct or indirect. You need to convert a decimal number into another number system in an indirect method (e.g. binary or hexadecimal), then you can convert it into binary number by converting each digit from hexadecimal into binary number and using grouping from the octal number system.

*Let’s understand it with example*

__98 into octal number__

First convert it into binary or hexadecimal number,

= (98)_{10}

= (1x2^{6}+1x2^{5}+0x2^{4}+0x2^{3}+0x2^{2}+1x2^{1}+0x2^{0})_{10 }*Binary Conversion*

= (6x16^{1}+2x16^{0})_{10 }*Hexadecimal Conversion*

*Because base of binary and hexadecimal are 2 and 16 respectively.*

= (1100010)_{2} *or* (62)_{16}

Then convert each digit of hexadecimal number into 4 bit of binary number whereas convert each group of 3 bits from least significant binary number.

= (001 100 010)_{2} *or* (0110 0010)_{2}

= (001 100 010)_{2}

= (1 4 2)_{8}

= (142)_{8}

That’s the one manual way of converting Decimal to Octal.

There are, however, two direct methods for converting a decimal number into an octal number: Converting to Remainders and Converting to Division. These are explained as below.

**Converting with Remainders (For integer part)****Converting with Remainders (For fractional part)**

This is a simple method involving dividing the number to be converted. Let decimal number is N then divide this number from eight because the octal number system base is eight. Note the remaining value will be: 0, 1, 2, 3, 4, 5, 6, or 7. Divide the remaining decimal number again until it has become 0 and note each remaining step. Then write remainders from the bottom up (or in reverse order), which will be the octal number of the decimal number given.

**Example** − Decimal 210 to octal number

210 / 8 = 26 **Remainder 2**

26 / 8 = 3 **Remainder 2**

3 / 8 = 0 **Remainder 3**

Now, write the remainder from the bottom up (in reverse order), this is 322 which is the equivalent octal number of decimal integer 210.

Let the decimal fraction part be M then multiply it by 8, as the octal number base is 8. Note the integral part value that is: 0, 1, 2, 3, 4, 5, 6, and 7. Again, multiply the remaining decimal number until it becomes 0 and note each integer of each step's result. Then write down the integer part results, which are the octal fraction number equal to the decimal number.

**Example** − Decimal fractional number 0.140869140625 to octal number

0.140869140625 x 8=0.12695313 **Resultant Integer 1**

0.12695313 x 8=0.01562504 **Resultant Integer 1**

0.01562504 x 8=0.12500032 **Resultant Integer 0**

0.12500032 x 8=0.00000256 **Resultant Integer 1**

0.00000256 x 8=0.000020544 **Resultant Integer 1**

*And so on…*

Now, write these resulting integer parts, 0.11010 which is the equivalent octal fractional number of 0.140869140625 decimal fractional.

You do not need to convert decimal to octal through these tough procedures as out decimal to octal converter is best in converting these numbers to each other. Our converter can convert integer and fractional decimal to octal easily and precisely.

For more conversions between binary, decimal, and hexadecimal numeric sysytem, you can use our free Decimal to Hex, Binary to Hex, Hex to Binary, Octal to Hex, Octal to Decimal converter.

Decimal | Octal |
---|---|

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 |

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