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| Number 10 | |
|---|---|
| Name | Ten |
| Numeral | 10 |
| Factorization | 2 × 5 |
| Divisors | 1, 2, 5, 10 |
| Prime | composite |
| Representation | decimal: 10; binary: 1010; roman: X |
Number 10
Ten, written as 10 in Hindu–Arabic numerals and as X in Roman numerals, is the base of the decimal system and a fundamental counting unit in many cultures. It appears across mathematics, science, measurement, culture, economics, sports, and computing, often serving as a conventional grouping or benchmark. The following sections examine its linguistic roots, arithmetic characteristics, scientific roles, symbolic meanings, and prominent usages.
The English word ten derives from Proto-Germanic *tehun and Proto-Indo-European *déḱm̥, paralleled by words such as German zehn, Dutch tien, Latin decem, Ancient Greek δέκα, Sanskrit दश (daśa), and Old Church Slavonic десеть (desętь). Numeral systems built on ten influenced the Arabic numerals adopted through transmission from Indian mathematics via scholars like Al-Khwarizmi and Al-Kindi, which in turn informed modern Western scripts. Written forms include the decimal 10, the Roman numeral X used by Roman Empire inscriptions and later European chronicles, and the tally marks found in many prehistoric and historic record-keeping traditions such as those in Mesopotamia and on the Lebombo bone.
Ten is the first double-digit integer in base ten and equals 2 × 5, making it the product of the first two distinct prime numbers, 2 and 5. It has four positive divisors and a sum-of-divisors σ(10)=18; its aliquot sum is 8 leading to the aliquot sequence 10, 8, 7, 1, 0 which connects to the study of perfect number theory and amicable pairs investigated by mathematicians such as Pierre de Fermat and Leonhard Euler. In base ten positional notation, powers of ten ((10^1, 10^2, 10^3, ...)) underpin place-value arithmetic formalized in works by Hindu–Arabic numeral scholars and later by Simon Stevin. Ten appears in various mathematical constructs including the decimal fraction, common logarithm (base 10) used by John Napier and later logarithm tables employed by scientists like Henry Briggs, and combinatorial structures such as 10-element sets referenced in theorems by Georg Cantor and enumeration problems studied by Gottfried Wilhelm Leibniz.
In the International System of Units maintained by BIPM, multiples and submultiples often use powers of ten such as kilo- (10^3) and milli- (10^-3) reflecting decimal scaling used in standards by Metre Convention signatories. The pH scale ranges typically around values like 1 to 14 where tenfold concentration differences correspond to one unit, a concept central to studies by S.P.L. Sørensen and biochemists such as Ernest Overton. Astronomical magnitude differences correspond to brightness ratios related to powers of ten studied by astronomers like Norman Pogson, while orders of magnitude in cosmology and particle physics (referenced by researchers at CERN and in work by Albert Einstein) use factors of ten to compare scales from 10^-35 m to 10^26 m.
Ten functions as a cultural benchmark across civilizations, appearing in canonical lists and legal codes such as the Ten Commandments central to Judaism and Christianity studies and discussed in theological commentaries by figures like St. Augustine and Rashi. Ten often symbolizes completeness or perfection in various traditions, reflected in constructs like the ten sefirot in Kabbalah scholarship, the ten avatars concept appearing in some Hindu narratives, and the tenets enumerated in civic and fraternal orders such as those of Freemasonry. In ritual and calendar contexts, the decadal grouping recurs in practices recorded by historians of Imperial China and in decadal observances noted in records from Ancient Rome.
Economically, round figures like ten-percent thresholds feature in policy debates and taxation rules across locales governed by institutions such as the International Monetary Fund and national treasuries; ten-year bonds and decadal indicators are standard in analyses by agencies including the World Bank and central banks like the Federal Reserve System. In sports, the number ten jersey is iconic in association football with legends such as Pelé, Diego Maradona, Lionel Messi, and Zinedine Zidane commonly wearing it; gymnastics, diving, and figure skating historically used perfect-ten scoring by bodies like the International Gymnastics Federation and International Skating Union before adopting revised systems. Popular culture references include titles and works such as films and songs that use the decimal term in marketing and narrative frameworks across industries centered in Hollywood, Bollywood, and global music markets tracked by organizations like IFPI.
In computing, ten in decimal contrasts with binary (base 2) where 10_2 represents two, and with hexadecimal (base 16) where 0xA represents ten; computer scientists and engineers at institutions like Bell Labs and Massachusetts Institute of Technology routinely convert between bases for low-level programming and data encoding. The prominence of decimal influenced character encodings such as those standardized by Unicode for numeral glyphs and legacy encodings used in systems from IBM mainframes to modern processors. Decimal arithmetic remains important in financial computing, prompting standards like IEEE 754-2008 decimal formats adopted by hardware and languages used in projects at companies including Intel and Oracle.
Category:Integers