- The base is five.
- There are five "digits": 0,1, 2, 3, 4 .
- Positions correspond to integer powers of five, starting with power 0 at the rightmost digit, and increasing right to left.
- The digit placed at a position shows how many times that power of five is included in the number.

The number "five" in base five is represented by "10" That is:

1× (five)^{1}+0× (five)^{0}

The base in any positional representation is written as "10" (assuming that the usual symbols 0, 1, ... are used). Here is a number represented in base five: 421. It means:

`421 = `**4** × five^{2} + **2** × five^{1} + **1** × five^{0}

Remember, the symbol "5" can not be used in the base five system. Actually, the above sum should be written as follows. (This looks just like base ten, but remember, here "10" is "five".)

421 = 4 × 10^{2}+ 2 × 10^{1}+ 1 × 10^{0}

To avoid confusion,
sometimes the base being used
is placed as a subscript:
421_{5} means that base 5 is being used.
It is conventional to show the subscript in base 10.

Fill in the table. Each row shows two representations of the same integer. The column on the left represents it in base five, the column on the right represents it in base ten (except you have to fill in that column.)

Base five Representation |
Base ten Representation |
---|---|

0 | |

1 | |

2 | |

3 | |

4 | |

10 | |

11 | |

12 |