Quinary

Quinary (also known as pental or base 5) is a Positional number system structured around the number 5 and its powers. Many calculators support quinary arithmetic alongside arithmetic in commonly used bases as binary, octal, decimal and hexadecimal.

Usage
Quinary is the third prime base. It is much less useful than the previous two prime bases (binary and ternary). Most of the usability of quinary comes from something having five possible states or pertaining to the number 5. In our decimal world, quinary is easy for humans to comprehend, this is mostly because 205=1010. Despite the lack of divisors, the alpha and omega numbers provide patterns for numbers with factors of 2, 4 and 3.

Irrational numbers
Here are the most commonly used irrational numbers expressed in quinary:

Multiplication table
The quinary multiplication table is simple, although considerably larger than that of quaternary. It contains 6 non-trivial products: 2*2=4, 2*3=11, 3*3=14, 2*4=13, 3*4=22 and 4*4=31. Quinary is the smallest natural base where 2*2=4 is true.

Exponentiation table
As quinary is a prime base, only powers of 10 are easy to remember.

Fractions table
As quinary is a prime base, only fractions with denominators that are powers of that prime will terminate.

Related number systems

 * Pentavigesimal digits correspond to 2 quinary digits.
 * Centepentavigesimal digits correspond to 3 quinary digits.
 * Negaquinary is the negative base corresponding to quinary.
 * Bijective quinary is the bijective base corresponding to quinary.
 * Skew quinary is the skew base corresponding to quinary.
 * Balanced quinary is the balanced base corresponding to quinary.