Quinary
Encyclopedia
Quinary is a numeral system
with five as the base. A possible origination of a quinary system is that there are five finger
s on either hand
. The base five is stated from 0-4
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, twenty-five
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, so its location between two composite numbers (4 and 6) does not help make its radix economy
better.
Today, the main usage of base 5 is as a biquinary system, which is decimal
using five as a sub-base. Another example of a sub-base system, is sexagesimal, base 60, which used 10 as a sub-base.
A decimal
system with 5 as a sub-base is called biquinary, and is found in Wolof
and Khmer
. A vigesimal
system with 5 as a sub-base is found in Nahuatl
and the Maya numerals
.
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.
The Chinese and Japanese 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.
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
with five as the base. A possible origination of a quinary system is that there are five finger
Finger
A finger is a limb of the human body and a type of digit, an organ of manipulation and sensation found in the hands of humans and other primates....
s on either hand
Hand
A hand is a prehensile, multi-fingered extremity located at the end of an arm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs...
. The base five is stated from 0-4
In the quinary place system, five numerals, from 0
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
to 4, are used to represent any real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
. According to this method, five is written as 10, twenty-five
25 (number)
25 is the natural number following 24 and preceding 26.-In mathematics:It is a square number, being 5² = 5 × 5. It is the smallest square that is also a sum of two squares: 25 = 3² + 4²...
is written as 100 and sixty
60 (number)
60 is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.-In mathematics:...
is written as 220.
As five is a prime number, only the reciprocals of the powers of five terminate, so its location between two composite numbers (4 and 6) does not help make its radix economy
Radix economy
Various proposals have been made to quantify the relative costs between using different radices in representing numbers, especially in computer systems.-Definition:...
better.
Today, the main usage of base 5 is as a biquinary system, which is decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
using five as a sub-base. Another example of a sub-base system, is sexagesimal, base 60, which used 10 as a sub-base.
Usage
Many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot and Saraveca. Of these, Gumatj is the only true "5–25" language known, in which 25 is the higher group of 5. The Gumatj numerals are shown below:| Number | Numeral |
|---|---|
| 1 | wanggany |
| 2 | marrma |
| 3 | lurrkun |
| 4 | dambumiriw |
| 5 | wanggany rulu |
| 10 | marrma rulu |
| 15 | lurrkun rulu |
| 20 | dambumiriw rulu |
| 25 | dambumirri rulu |
| 50 | marrma dambumirri rulu |
| 75 | lurrkun dambumirri rulu |
| 100 | dambumiriw dambumirri rulu |
| 125 | dambumirri dambumirri rulu |
| 625 | dambumirri dambumirri dambumirri rulu |
A decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
system with 5 as a sub-base is called biquinary, and is found in Wolof
Wolof language
Wolof is a language spoken in Senegal, The Gambia, and Mauritania, and is the native language of the Wolof people. Like the neighbouring languages Serer and Fula, it belongs to the Atlantic branch of the Niger–Congo language family...
and Khmer
Khmer language
Khmer , or Cambodian, is the language of the Khmer people and the official language of Cambodia. It is the second most widely spoken Austroasiatic language , with speakers in the tens of millions. Khmer has been considerably influenced by Sanskrit and Pali, especially in the royal and religious...
. A vigesimal
Vigesimal
The vigesimal or base 20 numeral system is based on twenty .- Places :...
system with 5 as a sub-base is found in Nahuatl
Nahuatl
Nahuatl is thought to mean "a good, clear sound" This language name has several spellings, among them náhuatl , Naoatl, Nauatl, Nahuatl, Nawatl. In a back formation from the name of the language, the ethnic group of Nahuatl speakers are called Nahua...
and the Maya numerals
Maya numerals
Maya Numerals were a vigesimal numeral system used by the Pre-Columbian Maya civilization.The numerals are made up of three symbols; zero , one and five...
.
Roman numerals
Roman numerals
The numeral system of ancient Rome, or Roman numerals, uses combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as:...
are a biquinary system. The numbers 1, 5, 10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, and 50
50 (number)
This article discusses the number fifty. For the year 50 CE, see 50. For other uses of 50, see 50 50 is the natural number following 49 and preceding 51.-In mathematics:...
are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX.
The Chinese and Japanese versions of the abacus
Abacus
The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of...
use a biquinary system to simulate a decimal system for ease of calculation.
Urnfield culture numerals
Urnfield culture numerals
During the beginning of the Urnfield culture, around 1200 BC, a series of votive sickles of bronze with marks that have been interpreted as a numeral system, appeared in Central Europe.-Discovery:...
and some tally mark systems are also biquinary.
Units of currencies
Currency
In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply...
are commonly partially or wholly biquinary.
External links
- Quinary Base Conversion, includes fractional part, from Math Is Fun