Decimal

Decimal (also known as base 10 or Denary) is a positional number system structured around the number 10 and its powers. Numbers are expressed as a sum of powers of 10 and their multiples.

Decimal is by far most used base in the world, as it is the base humans use in daily life. This wiki is also written in decimal.

Usage and History
Base 10 has been initially adopted by humans around 3000 BCE, initially through additive systems like the Egyptian numerals. The Greek numerals and Hebrew numerals followed shortly afterwards, then came the Roman Numerals circa 800 BCE. Finally, the Hindu-Arabic numerals were invented between the 1st century and 4th century CE, which are the numerals we use today. With it, came the true positional decimal system.

It is thought that the reason why decimal was chosen as the number base to use for humans is the fact that we have five fingers on each hand, which makes finger counting easy. As finger counting was probably the earliest method to count developed by humans, it makes sense that when moving to written language it was natural to use base 10.

Decimal is used by people all around the world, and is also taught in schools.

Advantages
10 is a semiprime, but it's one of the lowest semiprimes. Its prime factors structure is 2*5, which although worse than 2*3, is still second best. Base 10 lies in a category similar to semiprime bases base 6 (=2*3) and base 15 (3*5). As such, it has only 2 non-trivial factors: 2 and 5. Division by these factors is simple. 4 is 2 squared and 8 is 2 cubed, so we can also divide by 4 and 8 easily. The alpha and omega totatives of decimal are 9 and 11, and with 9 being 3 squared, simple divisibility rules exist for 3, 9, and 11. This means that decimal takes care of divisibility by all numbers from 1 to 12, with the exception of 7.

Disadvantages
The biggest disadvantage of base 10 is the lack of the factor of 3, making $$\{\frac{1}{3},\frac{1}{6},\frac{1}{9},\frac{1}{12},...\}$$repeating fractions. However, this is mitigated to some extent by the omega totative being 3 squared, which allows for easy divisibility checks and easy counting. Decimal also poorly handles 7, a trait it shares with dozenal.

Arithmetic tables
The arithmethic tables for base 10 are the standard we use today: the multiplication table everyone learns in school, the divisibility rules everyone learns in school, etc.

Related number systems

 * Roman numerals are an additive number system closely related to decimal and quinary.
 * Negadecimal is the negative base corresponding to decimal:
 * Vigesimal, base 20, is commonly considered a cousin of decimal because it has the same prime factors.
 * Centesimal digits correspond to 2 decimal digits.
 * Millesimal digits correspond to 3 decimal digits.