## How to convert Quinary to Octal

Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix systems. It has the advantage of not requiring any extra symbols as digits. It is also used for digital displays.

**Formula**

Follow these steps to convert a quinary number into octal form:

The simplest way is to convert the quinary number into decimal, then the decimal into octal form.

- Write the powers of 5 (1, 5, 25, 125, 625, and so on) beside the quinary digits from bottom to top.
- Multiply each digit by it's power.
- Add up the answers. This is the decimal solution.
- Divide the decimal number by 8.
- Get the integer quotient for the next iteration (if the number will not divide equally by 8, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 7.
- Repeat the steps from step 4. until the quotient is equal to 0.
- Write out all the remainders, from bottom to top. This is the octal solution.

Digit | Power | Multiplication |
---|---|---|

4 | 625 | 2500 |

1 | 125 | 125 |

3 | 25 | 75 |

2 | 5 | 10 |

0 | 1 | 0 |

Division | Quotient | Remainder |
---|---|---|

2710 / 8 | 338 | 6 |

338 / 8 | 42 | 2 |

42 / 8 | 5 | 2 |

5 / 8 | 0 | 5 |