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# 10 (number)

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 Title: 10 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 10 (number)

 ← 9 10 11 →
Cardinal ten
Ordinal 10th
(tenth)
Numeral system decimal
Factorization 2 × 5
Divisors 1, 2, 5, 10
Roman numeral X
Roman numeral (unicode) X, x
Greek prefix deca-/deka-
Latin prefix deci-
Binary 10102
Ternary 1013
Quaternary 224
Quinary 205
Senary 146
Octal 128
Duodecimal A12
Vigesimal A20
Base 36 A36
Chinese numeral 十，拾
Hebrew י (Yod)
Khmer ១០
Korean
Tamil
Thai ๑๐
Devanāgarī १०
Bangla ১০

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. The reason for the choice of ten is assumed to be that humans have ten fingers (digits).

## Contents

• Common usage and derived terms 1
• In mathematics 2
• In numeral systems 2.1
• Decimal system 2.1.1
• Roman numerals 2.1.2
• Positional numeral systems other than decimal 2.1.3
• List of basic calculations 2.2
• In science 3
• Astronomy 3.1
• In religion and philosophy 4
• In money 5
• In music 6
• In sports and games 7
• In technology 8
• In other fields 9
• References 11

## Common usage and derived terms

• A collection of ten items (most often ten years) is called a decade.
• 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.)

## 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.

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.

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. Because 10 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 5), a regular decagon is a constructible polygon.

Ten is also a triangular number, a centered triangular number, and a tetrahedral 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

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), 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
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 duodecimal X

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 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:

### Astronomy

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

## In religion and philosophy

The tetractys
• 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 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).
• 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 boxing, if the referees counts to 10 whether the boxer is unconscious or not, it will declare a winner by knockout.
• 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.
• Danica Patrick's car number in the NASCAR Sprint Cup Series.

The jersey number 10 has been retired by several North American sports teams in honor of past playing greats or other key figures, including Major League Baseball, the NBA, the NFL, and the NHL.

## In other fields

10 playing cards of all four suits

Ten is:

## References

1. ^ Exodus 20:2-13
2. ^ Deuteronomy 5:6-17
3. ^ [3]
4. ^ [4]
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