Numerical digit
For example, in the numeral 10.34 (written in base 10), The total value of the number is 1 ten, 0 ones, 3 tenths, and 4 hundredths.
This system was established by the 7th century in India,[11] but was not yet in its modern form because the use of the digit zero had not yet been widely accepted.
[11] By the 13th century, Western Arabic numerals were accepted in European mathematical circles (Fibonacci used them in his Liber Abaci).
Balanced ternary turns out to have some useful properties and the system has been used in the experimental Russian Setun computers.
[17] Several authors in the last 300 years have noted a facility of positional notation that amounts to a modified decimal representation.
In 1840 Augustin-Louis Cauchy advocated use of signed-digit representation of numbers, and in 1928 Florian Cajori presented his collection of references for negative numerals.
Despite the essential role of digits in describing numbers, they are relatively unimportant to modern mathematics.
[18] Nevertheless, there are a few important mathematical concepts that make use of the representation of a number as a sequence of digits.
In the process of casting out nines, both sides of the latter equation are computed, and if they are not equal, the original addition must have been faulty.
Repdigits are a generalization of repunits; they are integers represented by repeated instances of the same digit.
[23] The question of whether there are any Lychrel numbers in base 10 is an open problem in recreational mathematics; the smallest candidate is 196.
The Oksapmin culture of New Guinea uses a system of 27 upper body locations to represent numbers.
[25] To preserve numerical information, tallies carved in wood, bone, and stone have been used since prehistoric times.
[26] Stone age cultures, including ancient indigenous American groups, used tallies for gambling, personal services, and trade-goods.
About 3100 BC, written numbers were dissociated from the things being counted and became abstract numerals.
This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians.
Babylonian-style sexagesimal numeration is still used in modern societies to measure time (minutes per hour) and angles (degrees).
[34] Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC.
[35] The Roman empire used tallies written on wax, papyrus and stone, and roughly followed the Greek custom of assigning letters to various numbers.
[38] The Incan Empire ran a large command economy using quipu, tallies made by knotting colored fibers.
[39] Knowledge of the encodings of the knots and colors was suppressed by the Spanish conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region.
[42] From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo.
Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th century.
[43] The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's Liber Abaci of 1201.
[46] Leibniz had developed the concept early in his career, and had revisited it when he reviewed a copy of the I Ching from China.
