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Quinary (base5 or pental^{[1]}^{[2]}^{[3]}) is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand.
In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twentyfive is written as 100 and sixty is written as 220.
As five is a prime number, only the reciprocals of the powers of five terminate, although its location between two highly composite numbers (4 and 6) guarantees that many recurring fractions have relatively short periods.
Today, the main usage of base 5 is as a biquinary system, which is decimal using five as a subbase. Another example of a subbase system, is sexagesimal, base 60, which used 10 as a subbase.
Each quinary digit has log_{2}5 (approx. 2.32) bits of information.^{[4]}
Few calculators support calculations in the quinary system, except for some Sharp models (including some of the EL500W and EL500X series, where it is named the pental system^{[1]}^{[2]}^{[3]}) since about 2005, as well as the opensource scientific calculator WP 34S. The Python programming language supports conversion of a string to quinary using the int function. For example, if s='101' then the function print(int('101',5)) would return 26.^{[5]}
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✪ Economic Activities: Primary, Secondary, Tertiary, Quaternary, Quinary (AP Human Geography)

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Transcription
Contents
Comparison to other radices
×  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 
Quinary  0  1  2  3  4  10  11  12  13  14  20  21  22 

Binary  0  1  10  11  100  101  110  111  1000  1001  1010  1011  1100 
Decimal  0  1  2  3  4  5  6  7  8  9  10  11  12 
Quinary  23  24  30  31  32  33  34  40  41  42  43  44  100 
Binary  1101  1110  1111  10000  10001  10010  10011  10100  10101  10110  10111  11000  11001 
Decimal  13  14  15  16  17  18  19  20  21  22  23  24  25 
Decimal (periodic part)  Quinary (periodic part)  Binary (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 
Usage
Many languages^{[6]} use quinary number systems, including Gumatj, Nunggubuyu,^{[7]} Kuurn Kopan Noot,^{[8]} Luiseño^{[9]} and Saraveca. Gumatj is a true "5–25" language, in which 25 is the higher group of 5. The Gumatj numerals are shown below:^{[7]}
Number  Base 5  Numeral 

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 
In the video game Riven and subsequent games of the Myst franchise, the D'ni language uses a quinary numeral system.
Biquinary
A decimal system with 2 and 5 as a subbases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system. The numbers 1, 5, 10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX.
Most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary. Units of currencies are commonly partially or wholly biquinary.
Quadquinary
A vigesimal system with 4 and 5 as a subbases is found in Nahuatl, Kaktovik Inupiaq numerals and the Maya numerals.
See also
References
 ^ ^{a} ^{b} "Archived copy" (PDF). Archived (PDF) from the original on 20170712. Retrieved 20170605.CS1 maint: Archived copy as title (link)
 ^ ^{a} ^{b} "Archived copy" (PDF). Archived (PDF) from the original on 20160222. Retrieved 20170605.CS1 maint: Archived copy as title (link)
 ^ ^{a} ^{b} "Archived copy" (PDF). Archived (PDF) from the original on 20170712. Retrieved 20170605.CS1 maint: Archived copy as title (link)
 ^ "Log base 2: log base 2". logbase2.blogspot.ca. Archived from the original on 29 October 2017. Retrieved 5 May 2018.
 ^ "Convert base2 binary number string to int". Stack Overflow. Archived from the original on 24 November 2017. Retrieved 5 May 2018.
 ^ Harald Hammarström, Rarities in Numeral Systems: "Bases 5, 10, and 20 are omnipresent." doi:10.1515/9783110220933.11
 ^ ^{a} ^{b} Harris, John (1982), Hargrave, Susanne (ed.), "Facts and fallacies of aboriginal number systems" (PDF), Work Papers of SILAAB Series B, 8: 153–181, archived from the original (PDF) on 20070831
 ^ 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 0292755317.
External links
 Quinary Base Conversion, includes fractional part, from Math Is Fun
 Quinarypentavigesimal and decimal calculator, uses D'ni numerals from the Myst franchise, integers only, fanmade.