# Examples On Base 5 [Explained]

Base 5 has a number of digits from 0, 1, 2, 3, and 4. And the place values are 1, 5, 25, 125, 625, 3125, and so on. Having said this, I will be looking at some examples on base 5 i.e. converting from base 5 to another base and vice versa.

**How to Convert From Base 5 to Another Base and Vice Versa**

**42 base 5 to base 10**

Convert 42_{5} to decimal

Solution

In my introduction, I said the place values are 1, 5, 25, 125, etc. So, in this case I will only use 1 and 5 because we have two digits which are 4 and 2

42_{5} = 5(4) + 1(2) = 20 + 2 = 22

So, 42 base 5 to base 10 is 22

**Convert 42 base 5 to base three numeral**

Solution

The first thing to do here to convert to base 10 (decimal). The easiest way to go from one base to another is to first convert to base 10.

42_{5} = 5(4) + 1(2) = 20 + 2 = 22

Now, 22 can now be converted to base 3 using the tree method

3 | 22 |

3 | 7 R 1 |

3 | 2 R 1 |

0 R 2 |

The R means a reminder

Going from the bottom to the top, the answer will be 211 base 3 (211_{3})

**423 base 5 to base 10**

Convert 423_{5} to decimal

Solution

In this case I will only use 1, 5, and 25 because we have three digits which are 4, 2, and 3

423_{5} = 25(4) + 5(2) + 1(3) = 100 + 10 + 3 = 113

So, 423 base 5 to base 10 is 113

**43 base 10 to base 5**

Solution

43 is already in base ten, so we can use division method

5 | 43 |

5 | 8 R 3 |

5 | 1 R 3 |

0 R 1 |

Starting from the bottom to the top, we will have 133 base 5

So, 43 base 10 to base 5 is 133_{5}

**444 base 5 to base 2**

The simplest way is to first convert to decimal. And since there are three digits 4, 4, and 4, the bplace values will be 1, 5, and 25.

444_{5} = 25(4) + 5(4) + 1(4) = 100 + 20 + 4 = 124

Then we use division method to get the base 2

2 | 124 |

2 | 62 R 0 |

2 | 31 R 0 |

2 | 15 R 1 |

2 | 7 R 1 |

2 | 3 R 1 |

2 | 1 R 1 |

0 R 1 |

So, from the bottom to the top the answer will be 1111100 base 2

Therefore, 444 base 5 to base 2 is 1111100_{2}

If you have a question, you can drop your comment below.

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