### Base 5 Number System Lesson for Quinary

How to learn and do quinary conversion; the base 5 numbering system;– 0 1 2 3 4; complete lesson and lots of examples. Includes short table of most-searched-for quinary / base 5 questions and answers.

If you understand the decimal (base 10) number system we use in our everyday lives, then you already understand the quinary (base 5) number system. You just don’t know that you know yet.

We use the decimal (base 10) number system in our day-to-day living. Base 10 has ten numbers (0-9) and orders of magnitude are times 10. The lowest-order number represents itself times one. The next-order number represents itself times 10. The next order number represents itself times 10x10 or itself times 100. The next order number represents itself times 10x10x10 or itself times 1000. And so on.

An example would be the number 2417. This number means there are:

seven 1’s,

one 10,

four 100’s,

and two 1000’s.

Which represents 7 + 10 + 400 + 2000; for a total of 2417.

### The Quinary ( base 5 ) numbering system uses the same structure...

 Converting to and from Base 5 to Base 10 number systems
...the only difference being the order of magnitude. Base 5 has five numbers (0 1 2 3 4) and orders of magnitude are times five. The lowest-order number represents itself times one. The next-order number represents itself times 5. The next order number represents itself times 5x5 or itself times 25. The next order of magnitude would be 5x5x5 or 125. And so on.

An example would be the number 3142. This number means there are...

two 1’s,

four 5’s,

one 25,

and three 125's.

Which represents 2 + 20 + 25 + 375 for a total of 422.

Another example would be the number 2011. This number means there are...

One 1,

one 5,

no 25's,

and two 125's.

Which represents 1 + 5 + 0 + 250; for a total of 256.

### Some of the most-searched-for Questions and Answers:

• What is 5 (base 10) in base 5? Answer is 10 in base 5.
• What is 10 (base 10) in base 5? Answer is 20 in base 5.
•  What is 23 (base 10) in base 5? Answer is 43 in base 5.
•  What is 25 (base 10) in base 5? Answer is 100 in base 5.
•  What is 27 (base 10) in base 5? Answer is 102 in base 5.

### More Base 5 to Base 10 Numbering System Conversion Examples

#### Quinary / Base 5 Orders of Magnitude

1 - 5 - 25 - 125 - 625 - 3125 - 15625 - 78125 - 390625 - 1953125

#### Positional

1953125 - 390625 - 78125 - 15625 - 3125 - 625 - 125 - 25 - 5 - 1
List of Base 5 Examples
• 1 = 1
• 2 = 2
• 3 = 3
• 4 = 4
• 10 = 5
• 11 = 6
• 12 = 7
• 13 = 8
• 14 = 9
• 20 = 10
• 21 = 11
• 22 = 12
• 23 = 13
• 24 = 14
• 30 = 15
• 31 = 16
• 32 = 17
• 33 = 18
• 34 = 19
• 40 = 20
• 41 = 21
• 42 = 22
• 43 = 23
• 44 = 24
• 100 = 25

#### Quinary / Base 5 Orders of Magnitude (convenience relist)

1 - 5 - 25 - 125 - 625 - 3125 - 15625 - 78125 - 390625 - 1953125

#### Positional

1953125 - 390625 - 78125 - 15625 - 3125 - 625 - 125 - 25 - 5 - 1
List of More Base 5 Examples
• 100 = 25
• 101 = 26
• 200 = 50
• 220 = 60
• 222 = 62
• 300 = 75
• 303 = 78
• 333 = 93
• 404 = 104
• 420 = 110
• 1000 = 125
• 1001 = 126
• 1010 = 130
• 1100 = 150
• 1234 = 1194
• 2020 = 2v60
• 2030 = 265
• 3020 = 385
• 3411 = 481
• 4000 = 500
• 4040 = 520
• 4242 = 572
• 4321 = 586
• 4333 = 593
• 4444 = 624

#### Quinary / Base 5 Orders of Magnitude (convenience relist)

1 - 5 - 25 - 125 - 625 - 3125 - 15625 - 78125 - 390625 - 1953125

#### Positional

1953125 - 390625 - 78125 - 15625 - 3125 - 625 - 125 - 25 - 5 - 1