10th

This article is about the number. For other uses of 'ten', see Ten (disambiguation). For other uses of the ordinal 10th, see Tenth (disambiguation).

10 (ten numbers in both spoken and written language. The reason for the choice of ten is assumed to be that humans have ten fingers (digits).

In common usage and derived terms

  • A collection of ten items (most often ten years) is called a decade.
  • The ordinal 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.)
  • With ten being the base of the decimal system, a scale of 1 to 10 is often used to rank things, as a smaller version of a 1-to-100 scale (as is used in percentages and wine-tasting). Hence, something that scores perfectly is "a perfect ten". A person who is attractive and physically flawless is often said to be "a ten", from the idea of ranking that person's appearance and sex-appeal on a 1-to-10 scale.[citation needed]

In mathematics

Ten is a composite number, 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.

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.

It is the aliquot sum of only one number the discrete semiprime 14.

Ten is a semi-meandric number.

Ten is the sum of the first three prime numbers, of the four first numbers (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.

A polygon with ten sides is a decagon, and 10 is a decagonal number. But it is also a triangular number and a centered triangular number.

Ten is the number of n-Queens Problem solutions for n = 5.

Ten is the smallest number whose status as a possible friendly number is unknown.

In numeral systems

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 V's [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed). Incidentally, the Chinese word numeral for ten, is also a cross: .

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
Base Numeral system Number
1 unary **********
2 binary 1010
3 ternary 101
4 quaternary 22
5 quinary 20
6 senary 14
7 septenary 13
8 octal 12
9 novenary 11
10 decimal 10
12 dozenal X
16 hexadecimal A

Properties:

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 \times 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 \div x 10 5 3.\overline{3} 2.5 2 1.\overline{6} 1.\overline{428571} 1.25 1.\overline{1} 1 0.\overline{90} 0.8\overline{3} 0.\overline{769230} 0.\overline{714285} 0.\overline{6}
x \div 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
10 ^ x\, 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000
x ^ {10}\, 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 3486784401 10000000000

In science

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:

Astronomy

  • The Sculptor.
  • The solar eclipse series which began on -2467 February 28 and ended on -1169 April 18. The duration of Saros series 10 was 1298.1 years, and it contained 73 solar eclipses.
  • The Saros lunar eclipse series which began on -2454 June 17 and ended on -1138 August 15. The duration of Saros series 10 was 1316.2 years, and it contained 74 lunar eclipses.

In religion and philosophy

  • In Pythagoreanism, the number 10 played an important role and was symbolized by the tetractys.
  • In Hinduism, Lord Maha Vishnu appeared on the earth in 10 incarnations.

In money

Most countries issue coins and bills with a denomination of 10 (See e.g. 10 dollar note). Of these, the 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

In sports and games

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

  • decathlon, a combined event in athletics consisting of ten track and field events.

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

  • In American football, the end zones are 10 yards deep.
  • In association football, the number 10 is traditionally worn by the team's playmaker. This use has led to "Number 10" becoming a synonym for that particular player, even if he or she does not wear that number.
  • In Australian rules football, considered the break even amount of games won in a regular 22 game season.
  • In baseball, 10 is the minimum number of players on the field at any given time during play (including the batter).
  • In basketball:
    • The top of the rim (goal) is 10 feet from the floor.
    • In standard full-court basketball, there are 10 players on the court (5 on each team).
  • In blackjack, the Ten, Jack, Queen and King are all worth 10 points.
  • In cricket, 10 is the number of wickets required to be taken by the bowling side for the batting side to be bowled out.
  • In gridiron football, 10 is the number of yards the offense must advance to maintain possession in a single set of downs—four in American and three in Canadian.
  • In most rugby league competitions, the number 10 is worn by one of the two starting props. (One exception to this rule is the European 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.
  • The highest score possible in Olympics gymnastics competitions.
  • Driving a racing car at ten-tenths is driving as fast as possible, on the limit.

The jersey number 10 has been retired by several North American sports teams in honor of past playing greats or other key figures:

In technology

In other fields

Ten is:

See also

References

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.