Definitions

# 10 (number)

10 (ten) is an even natural number following 9 and preceding 11.

## In mathematics

Ten is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that can not be expressed as the difference between any integer and the total number of coprimes below it.

Ten is the second discrete biprime (2.5) and the second member of the (2.q) discrete biprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete biprime to be in deficit. All subsequent discrete biprimes 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 biprime 14.

Ten is a semi-meandric number.

Ten is the sum of the first three prime numbers and also of the first four factorials. Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.

Ten squared equals 100.

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.

### In numeral systems

Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language. 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). The reason for the choice of ten is assumed to be that humans have ten fingers (digits).

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

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). The Chinese word numeral for ten is 十, which resembles a cross.

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

Ten is a Harshad number in bases 2, 3, 5, 6, 9 and all others above.

### 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 $3.overline\left\{3\right\}$ 2.5 2 $1.overline\left\{6\right\}$ $1.overline\left\{4\right\}2857overline\left\{1\right\}$ 1.25 $1.overline\left\{1\right\}$ 1 $0.overline\left\{9\right\}overline\left\{0\right\}$ $0.8overline\left\{3\right\}$ $0.overline\left\{7\right\}6923overline\left\{0\right\}$ $0.overline\left\{7\right\}1428overline\left\{5\right\}$ $0.overline\left\{6\right\}$
$x div 10$ 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 11 12 13
$10 ^ x,$ 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000
$x ^ \left\{10\right\},$ 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 3486784401 10000000000 25937424601 61917364224 137858491849

## In music

• The interval of a major or minor tenth is an octave plus a major or minor third.
• The title of quite a few albums, including recordings by Pearl Jam and LL Cool J. See Ten (album).

## Age 10

• Minimum age at which can watch a TV-PG show without parental consent.
• Minimum age at which can watch a 10-rated show or movie in Brazil without parental consent.
• Minimum age at which can rent, buy or play a E10+ rated game by the ESRB without parental consent.

## In other fields

• Number of incarnations of The Doctor in the BBC science fiction television program Doctor Who
• Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten.
• The number of theatrical Star Trek films that have been released so far.
• A collection of ten items (most often ten years) is called a decade.
• A decapod crustacean has ten limbs.
• 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).
• Blake Edwards' 1979 movie 10.
• 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. For example, in the movie 10 Bo Derek is supposedly a "10" on that scale.
• Counting from one to ten before speaking is often done in order to cool one's temper.
• In astrology, Capricorn is the 10th astrological sign of the Zodiac.
• In Chinese astrology, the 10 Heavenly Stems, refer to a cyclic number system that is used also for time reckoning.
• The ordinal adjective is denary.
• An online show hosted by Microsoft.
• Ben 10 is a show about a boy that can transform into 10 aliens.
• A 1977 short documentary film Powers of Ten depicts the relative scale of the Universe in factors of ten (orders of magnitude).
• CBS has a game show called Power of 10, where the player's prize goes up and down by either the previous or next power of ten.
• There are ten official inkblots in the Rorschach inkblot test.
• The traditional Snellen chart uses 10 different letters.

Ten is:

## Historical years

10 A.D., 10 B.C., 1910, 2010, etc.