10 (number)

← 9 11 → 10
← 10 11 12 13 14 15 16 17 18 19 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	10 ten
Ordinal	10th (tenth)
Numeral system	decimal
Factorization	$2\cdot5$
Divisors	1, 2, 5, 10
Roman numeral	X
Unicode symbol(s)	X, x
Greek	ι, Ι
Greek Prefix	deca-/deka-
Latin Prefix	deci-
Binary	1010₂
Octal	12₈
Duodecimal	A₁₂
Hexadecimal	A₁₆
----
Chinese numeral	十，拾
Hebrew	י (Yod)
Khmer	១០
Korean	십
Tamil	௰
Thai	๑๐
Hindi	१० (Dush)
Bangla	১০ (দশ)
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10 (ten ⁱ/ˈtɛn/) is an even natural number following 9 and preceding 11.

1 In common usage and derived terms
2 In mathematics
- 2.1 In numeral systems
- 2.2 List of basic calculations
3 In science
- 3.1 Astronomy
4 In religion and philosophy
5 In money
6 In music
7 In sports and games
8 In technology
9 In other fields
10 Historical years
11 See also
12 References

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.

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

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).

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 a cross, too: 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
16	hexadecimal	A

Properties:

Ten is a Harshad number in bases 2, 3, 5, 6, 9 and all others above.
In bases 15, 18 and 30, ten is a 1-automorphic number (displayed as the numeral 'A')..

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		$0.\overline{9}\overline{0}$	$0.8\overline{3}$	$0.\overline{769230}$	$0.\overline{714285}$	$0.\overline{6}$
$x \div 10$	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:

The atomic number of neon.
The number of hydrogen atoms in butane, a hydrocarbon.
The number of spacetime dimensions in some superstring theories.

Astronomy

The New General Catalogue object NGC 10, a magnitude 12.5 spiral galaxy in the constellation Sculptor.

The Saros number of 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 number of the 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.

Messier object M10, a magnitude 6.4 globular cluster in the constellation Ophiuchus.

In religion and philosophy

References in the Bible, Judaism and Christianity:
- The Ten Commandments of Exodus^[1] and Deuteronomy^[2] are considered a cornerstone of Judaism and Christianity.
- People traditionally tithed one-tenth of their produce. The practice of tithing is still common in Christian churches today, though it is disputed in some circles as to whether or not it is required of Christians.
- In Deuteronomy 26:12, the Torah commands Jews to give one-tenth of their produce to the poor (Maaser Ani). From this verse and from an earlier verse (Deut. 14:22) there derives a practice for Jews to give one-tenth of all earnings to the poor.^[3]
- Ten Plagues were inflicted on Egypt in Exodus 7-12
- Jews observe the annual Ten Days of Repentance beginning on Rosh Hashanah and ending on Yom Kippur.
- In Jewish liturgy, Ten Martyrs are singled out as a group.
- There are said to be Ten Lost Tribes of Israel (those other than Judah and Benjamin)
- There are Ten Sephirot in the Kabbalistic Tree of Life
- The Bible records 10 generations between Adam and Noah, and 10 generations between Noah and Abraham
- In Judaism, ten adults are the required quorum for prayer services.

In Pythagoreanism, the number 10 played an important role and was symbolized by the tetractys.

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

The interval of a major tenth is an octave plus a major third.
The interval of a minor tenth is an octave plus a minor third.
The title of quite a few albums. See Ten (album).
"Ten lords a-leaping" is the gift on the tenth day of Christmas in the carol "The Twelve Days of Christmas"

In sports and games