# 五進制

## 同其他進制嘅比較

 × 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
五進制 二進制 十進制 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 10 11 12 13 14 20 21 22 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 23 24 30 31 32 33 34 40 41 42 43 44 100 1101 1110 1111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001
 十進制 (循環節) 五進制 (循環節) 二進制 (循環節) 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

## 語言

1 1 wanggany
2 2 marrma
3 3 lurrkun
4 4 dambumiriw
5 10 wanggany rulu
6 11 wanggany rulu ga wanggany
7 12 wanggany rulu ga marrma
8 13 wanggany rulu ga lurrkun
9 14 wanggany rulu ga dambumiriw
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

## 雙五進制

 I V X L C D M 1 5 10 50 100 500 1000

「二五進制編碼十進數」係一啲早期嘅電腦，例如ColossusIBM 650呢啲用雙五進制嚟記十進制數字嘅方法。

## 四五進制

Nahuatl用一種以4、5做sub-base嘅二十進制。[8]

## 計數機同程式語言

Python嘅`int()`函數可以將任何進制嘅數轉返做十進制，例如五進制嘅101可以用`int('101',5)`轉返做十進制嘅26[9]

## 參考資料

1. "Archived copy" (PDF). 原先內容歸檔 (PDF)喺2017-07-12. 喺2017-06-05搵到.`{{cite web}}`: CS1 maint: archived copy as title (link)
2. "Archived copy" (PDF). 原先內容歸檔 (PDF)喺2016-02-22. 喺2017-06-05搵到.`{{cite web}}`: CS1 maint: archived copy as title (link)
3. "Archived copy" (PDF). 原先內容歸檔 (PDF)喺2017-07-12. 喺2017-06-05搵到.`{{cite web}}`: CS1 maint: archived copy as title (link)
4. Harald Hammarström, Rarities in Numeral Systems: "Bases 5, 10, and 20 are omnipresent."
5. Harris, John (1982), Hargrave, Susanne (編), "Facts and fallacies of aboriginal number systems" (PDF), Work Papers of SIL-AAB Series B, 8: 153–181, 原著 (PDF)喺2007-08-31歸檔
6. Dawson, J. "Australian Aborigines: The Languages and Customs of Several Tribes of Aborigines in the Western District of Victoria (1881), p. xcviii.
7. Closs, Michael P. Native American Mathematics. ISBN 0-292-75531-7.
8. "Numbers in Nahuatl". omniglot.com. 喺2022-05-19搵到.
9. "Convert base-2 binary number string to int". Stack Overflow. 原先內容歸檔喺24 November 2017. 喺5 May 2018搵到.