五進制是以5為底的進位制，主因乃人類的一隻手有五隻手指。
在五進制中，有五個數字，各是0、1、2、3、4，用來代表各種實數，
依此規則，十進制的5，在五進制中為10。
在二十世紀中，只有肯亞和奈及利亞的約魯巴人仍在使用這種五進制的系統，
不過，十進制在各地區已普遍使用，這些部落原本使用的五進制，也已慢慢消逝。另一方面，在西歐普遍流行的二十進制，亦被視為一種特殊的五進制特例。
Qui
（五進） |
Bin
（二進） |
Dec
（十進）
|
| 0 |
0000 |
0
|
| 1 |
0001 |
1
|
| 2 |
0010 |
2
|
| 3 |
0011 |
3
|
| 4 |
0100 |
4
|
| 10 |
0101 |
5
|
| 11 |
0110 |
6
|
| 12 |
0111 |
7
|
| 13 |
1000 |
8
|
| 14 |
1001 |
9
|
| 20 |
1010 |
10
|
| 21 |
1011 |
11
|
| 22 |
1100 |
12
|
| 23 |
1101 |
13
|
| 24 |
1110 |
14
|
| 30 |
1111 |
15
|
比較
五進制乘法表
| × |
1 |
2 |
3 |
4 |
10 |
11 |
12 |
13 |
14 |
20
|
| 1 |
1 |
2 |
3 |
4 |
10 |
11 |
12 |
13 |
14 |
20
|
| 2 |
2 |
4 |
11 |
13 |
20 |
22 |
24 |
31 |
33 |
40
|
| 3 |
3 |
11 |
14 |
22 |
30 |
33 |
41 |
44 |
102 |
110
|
| 4 |
4 |
13 |
22 |
31 |
40 |
44 |
103 |
112 |
121 |
130
|
| 10 |
10 |
20 |
30 |
40 |
100 |
110 |
120 |
130 |
140 |
200
|
| 11 |
11 |
22 |
33 |
44 |
110 |
121 |
132 |
143 |
204 |
220
|
| 12 |
12 |
24 |
41 |
103 |
120 |
132 |
144 |
211 |
223 |
240
|
| 13 |
13 |
31 |
44 |
112 |
130 |
143 |
211 |
224 |
242 |
310
|
| 14 |
14 |
33 |
102 |
121 |
140 |
204 |
223 |
242 |
311 |
330
|
| 20 |
20 |
40 |
110 |
130 |
200 |
220 |
240 |
310 |
330 |
400
|
標準五進制中的數字 0 到 25
| 五進制
|
0 |
1 |
2 |
3 |
4 |
10 |
11 |
12 |
13 |
14 |
20 |
21 |
22
|
| 二進制
|
0 |
1 |
10 |
11 |
100 |
101 |
110 |
111 |
1000 |
1001 |
1010 |
1011 |
1100
|
| 十進制
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
|
|
| 五進制
|
23 |
24 |
30 |
31 |
32 |
33 |
34 |
40 |
41 |
42 |
43 |
44 |
100
|
| 二進制
|
1101 |
1110 |
1111 |
10000 |
10001 |
10010 |
10011 |
10100 |
10101 |
10110 |
10111 |
11000 |
11001
|
| 十進制
|
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25
|
五進制分數
| 十進制 (periodic part) |
五進制 (periodic part)
|
二進制 (periodic part)
|
| 1/2 = 0.5
|
1/2 = 0.2
|
1/10 = 0.1
|
| 1/3 = 0.3
|
1/3 = 0.13
|
1/11 = 0.01
|
| 1/4 = 0.25
|
1/4 = 0.1
|
1/100 = 0.01
|
| 1/5 = 0.2
|
1/10 = 0.1
|
1/101 = 0.0011
|
| 1/6 = 0.16
|
1/11 = 0.04
|
1/110 = 0.010
|
| 1/7 = 0.142857
|
1/12 = 0.032412
|
1/111 = 0.001
|
| 1/8 = 0.125
|
1/13 = 0.03
|
1/1000 = 0.001
|
| 1/9 = 0.1
|
1/14 = 0.023421
|
1/1001 = 0.000111
|
| 1/10 = 0.1
|
1/20 = 0.02
|
1/1010 = 0.00011
|
| 1/11 = 0.09
|
1/21 = 0.02114
|
1/1011 = 0.0001011101
|
| 1/12 = 0.083
|
1/22 = 0.02
|
1/1100 = 0.0001
|
| 1/13 = 0.076923
|
1/23 = 0.0143
|
1/1101 = 0.000100111011
|
| 1/14 = 0.0714285
|
1/24 = 0.013431
|
1/1110 = 0.0001
|
| 1/15 = 0.06
|
1/30 = 0.013
|
1/1111 = 0.0001
|
| 1/16 = 0.0625
|
1/31 = 0.0124
|
1/10000 = 0.0001
|
| 1/17 = 0.0588235294117647
|
1/32 = 0.0121340243231042
|
1/10001 = 0.00001111
|
| 1/18 = 0.05
|
1/33 = 0.011433
|
1/10010 = 0.0000111
|
| 1/19 = 0.052631578947368421
|
1/34 = 0.011242141
|
1/10011 = 0.000011010111100101
|
| 1/20 = 0.05
|
1/40 = 0.01
|
1/10100 = 0.000011
|
| 1/21 = 0.047619
|
1/41 = 0.010434
|
1/10101 = 0.000011
|
| 1/22 = 0.045
|
1/42 = 0.01032
|
1/10110 = 0.00001011101
|
| 1/23 = 0.0434782608695652173913
|
1/43 = 0.0102041332143424031123
|
1/10111 = 0.00001011001
|
| 1/24 = 0.0416
|
1/44 = 0.01
|
1/11000 = 0.00001
|
| 1/25 = 0.04
|
1/100 = 0.01
|
1/11001 = 0.00001010001111010111
|
用途
在许多语言中[1]都会使用五进制，其中包括古马其语[2]、农古布尤语[2]、库恩科潘努特语[3]、路易斯语[4]、萨拉韦卡语。而古马其语是一种真正的“5-25”语言，其中25是5中较高的一组，古马其语数字系统[2]如下所示：
| 十进制
|
五进制
|
数字名称
|
| 1
|
1
|
wanggany
|
| 2
|
2
|
marrma
|
| 3
|
3
|
lurrkun
|
| 4
|
4
|
dambumiriw
|
| 5
|
10
|
wanggany rulu
|
| 10
|
20
|
marrma rulu
|
| 15
|
30
|
lurrkun rulu
|
| 20
|
40
|
dambumiriw rulu
|
| 25
|
100
|
dambumirri rulu
|
| 50
|
200
|
marrma dambumirri rulu
|
| 75
|
300
|
lurrkun dambumirri rulu
|
| 100
|
400
|
dambumiriw dambumirri rulu
|
| 125
|
1000
|
dambumirri dambumirri rulu
|
| 625
|
10000
|
dambumirri dambumirri dambumirri rulu
|
參考
- ^ Harald Hammarström, Rarities in Numeral Systems: "Bases 5, 10, and 20 are omnipresent." doi:10.1515/9783110220933.11
- ^ 2.0 2.1 2.2 Harris, John, Hargrave, Susanne , 编, Facts and fallacies of aboriginal number systems (PDF), Work Papers of SIL-AAB Series B, 1982, 8: 153–181, （原始内容 (PDF)存档于2007-08-31）
- ^ Dawson, J. "Australian Aborigines: The Languages and Customs of Several Tribes of Aborigines in the Western District of Victoria (1881), p. xcviii.
- ^ Closs, Michael P. Native American Mathematics
. ISBN 0-292-75531-7.
