10

10 (ten) is an even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language. It is the first double-digit number. The reason for the choice of ten is assumed to be that humans have ten fingers (digits).

This article is about the number. For the year, see AD 10. For other uses of "ten", see Ten (disambiguation). For other uses of the ordinal 10th, see Tenth (disambiguation).
← 9 10 11 →
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Cardinalten
Ordinal10th
(tenth)
Numeral systemdecimal
Factorization2 × 5
Divisors1, 2, 5, 10
Greek numeralΙ´
Roman numeralX
Roman numeral (unicode)X, x
Greek prefixdeca-/deka-
Latin prefixdeci-
Binary10102
Ternary1013
Octal128
DuodecimalA12
HexadecimalA16
Chinese numeral十，拾
Hebrewי (Yod)
Khmer១០
Tamil௰
Thai๑๐
Devanāgarī१०
Bengali১০
Arabic & Kurdish١٠

Anthropology

Usage and terms
  • A collection of ten items (most often ten years) is called a decade.
  • The ordinal adjective is decimal; the distributive adjective is denary.
  • Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten.
  • To reduce something by one tenth is to decimate. (In ancient Rome, the killing of one in ten soldiers in a cohort was the punishment for cowardice or mutiny; or, one-tenth of the able-bodied men in a village as a form of retribution, thus causing a labor shortage and threat of starvation in agrarian societies.)
  • Ten is used as a theoretical highest number in topics that require a rating ("a mark out of ten"), by contrast having 0 or 1 as the lowest number, and 5 being average.

Other
See also: List of highways numbered 10

In mathematics
  • Ten is a composite number with 4 divisors, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.[1]
  • Ten is the second discrete semiprime (2 × 5) and the second member of the (2 × q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree.
  • Ten is the smallest semiprime that is the sum of all the distinct prime numbers from its lower factor through its higher factor (10 = 2 + 3 + 5 = 2 . 5) Only three other small semiprimes (39, 155, and 371) share this attribute.
  • Ten is the sum of the first three prime numbers, of the four first positive integers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.
  • Ten is the smallest number whose status as a possible friendly number is unknown.
  • Ten factorial seconds is exactly equal to 6 weeks.
  • According to a conjecture, ten is the average sum of the proper divisors of the natural numbers if the size of the numbers approaches infinity (sequence A297575 in the OEIS).
  • Ten is the smallest number whose fourth power can be written as a sum of two squares in two different ways. (802 + 602 and 962 + 282)

Decimal system
Main article: Decimal

As is the case for any base in its system, ten is the first two-digit number in decimal and thus the lowest number where the position of a numeral affects its value. Any integer written in the decimal system can be multiplied by ten by adding a zero to the end (e.g. 855 × 10 = 8550).

Roman numerals

The Roman numeral for ten is X (which looks like two Vs [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed), and X for ten from both hands. Incidentally, the Chinese word numeral for ten, is also a cross: 十.

Positional numeral systems other than decimal

The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.)

Representation of 10 in other bases
BaseNumeral systemNumber
1unary**********
2binary1010
3ternary101
4quaternary22
5quinary20
6senary14
7septenary13
8octal12
9novenary11
10decimal10
12duodecimalX
16hexadecimalA

List of basic calculations
Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 50 100 1000
10 × x 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 250 500 1000 10000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10 ÷ x 10 5 3.3 2.5 2 1.6 1.428571 1.25 1.1 1 0.90 0.83 0.769230 0.714285 0.6
x ÷ 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Exponentiation 1 2 3 4 5 6 7 8 9 10
10x 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000
x10 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 3486784401 10000000000

In science

The SI prefix for 10 is "deca-".

The meaning "10" is part of the following terms:

  • decapoda, an order of crustaceans with ten feet.
  • decane, a hydrocarbon with 10 carbon atoms.

Also, the number 10 plays a role in the following:

The metric system is based on the number 10, so converting units is done by adding or removing zeros (e.g. 1 centimeter = 10 millimeters, 1 decimeter = 10 centimeters, 1 meter = 100 centimeters, 1 dekameter = 10 meters, 1 kilometer = 1,000 meters).

Astronomy

In religion and philosophy
The tetractys

In money

Most countries issue coins and bills with a denomination of 10 (See e.g. 10 dollar note). Of these, the U.S. dime, with the value of ten cents, or one tenth of a dollar, derives its name from the meaning "one-tenth" − see Dime (United States coin)#Denomination history and etymology.

In music
See also: Ten (disambiguation) § Art and entertainment

In sports and games
  • Decathlon is a combined event in athletics consisting of ten track and field events.
  • In association football, the number 10 is traditionally worn by the team's advanced playmaker. This use has led to "Number 10" becoming a synonym for the player in that particular role, even if he or she does not wear that number.[8]
  • In gridiron football, a team has a limited number of downs to advance the ball ten yards or more from where it was on its last first down; doing this is referred to as gaining another first down.
  • In auto racing, driving a car at ten-tenths is driving as fast as possible, on the limit.
  • In basketball, each quarter runs for 10 minutes under FIBA, WNBA, and NCAA women's rules.
  • In blackjack, the Ten, Jack, Queen and King are all worth 10 points.
  • In boxing, if the referee counts to 10 whether the boxer is unconscious or not, it will declare a winner by knockout.
  • In cricket, a team's innings ends once it has lost 10 wickets.
  • In men's field lacrosse, each team has 10 players on the field at any given time, except in penalty situations.
  • In most rugby league competitions, the number 10 is worn by one of the two starting props. One exception to this rule is the Super League, which uses static squad numbering.
  • In rugby union, the starting fly-half wears the 10 shirt.
  • In ten-pin bowling, 10 pins are arranged in a triangular pattern and there are 10 frames per game.

In technology
  • Ten-codes are commonly used on emergency service radio systems.
  • Ten refers to the "meter band" on the radio spectrum between 28 and 29.7 MHz, used by amateur radio.
  • ASCII and Unicode code point for line feed.
  • In MIDI, Channel 10 is reserved for unpitched percussion instruments.
  • In the Rich Text Format specification, all language codes for regional variants of the Spanish language are congruent to 10 mod 256.
  • In macOS, the F10 function key tiles all the windows of the current application and grays the windows of other applications.
  • The IP addresses in the range 10.0.0.0/8 (meaning the interval between 10.0.0.0 and 10.255.255.255) is reserved for use by private networks by RFC 1918.

Age 10
  • This is generally the age when a child enters the preteen stage and also a denarian (someone within the age range of 10-19).
  • The ESRB recommends video games with an E10+ rating to children aged 10 and up.

In other fields
10 playing cards of all four suits

See also
  • Mathematics portal

References
  1. "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  2. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  3. "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  4. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  5. Exodus 20:2–13
  6. Deuteronomy 5:6–17
  7. Archived February 23, 2006, at the Wayback Machine
  8. Khalil Garriot (21 June 2014). "Mystery solved: Why do the best soccer players wear No. 10?". Yahoo. Retrieved 19 May 2015.
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