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

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

10 | 5 |

11 | 6 |

12 | 7 |

You
may wish to change the __representation__ of a number
from base 5 notation into base 10 notation.
Do this by symbol replacement.
Change the base 5 symbols into the base 10 symbol
equivalents.
Then do the arithmetic in base 10.

`421` | = | ` 4 × five` |

the number in base 10 | = | ` 4 × 5` |

the number in base 10 | = | ` 4 × 25 + 2 × 5 + 1 × 1` |

the number in base 10 | = | ` 100 + 10 + 1 = 111` |

The above process is often called "converting a number from base 5 to base 10".
But in fact, the *number* is not being converted,
its *representation* is
being converted.
The characters "421 (base five)" and "111 (base ten)" represent the *same number*.

Change the representation of 102_{5} from base five to base ten.