# 10 (number)

11
10

10 11 12 13 14 15 16 17 18 19

0 10 20 30 40 50 60 70 80 90 >>

Cardinal ten
Ordinal 10th
(tenth)
Numeral system decimal
Factorization $2\cdot5$
Divisors 1, 2, 5, 10
Roman numeral X
Unicode symbol(s) X, x
Greek Prefix deca-/deka-
Latin Prefix deci-
Binary 10102
Octal 128
Duodecimal A12
----
Chinese numeral 十，拾
Hebrew י (Yod)
Khmer ១០
Korean
Thai ๑๐

10 (ten) is a natural number[1] that follows 9 and precedes 11. It is an integer and a cardinal number, that is, a number that is used for counting.[2] In addition, it is classified as a real number,[3] distinguishing it from imaginary numbers. Ten is the base of the decimal system. It is the total number of digits on a person's two hands or two feet.

## 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

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

## In science

### Biology

• Normally, ten is the number of digits a person has on both hands (taken together) or both feet (taken together).

### Astronomy

• Ten is the Saros number[4] of the solar eclipse series that began on February 28, 2467 B.C.E. and ended on April 18, 1169 B.C.E. The duration of Saros series 10 was 1298.1 years, and it contained 73 solar eclipses.
• Ten is the Saros number[5] of the lunar eclipse series that began on June 17, 2454 B.C.E. and ended on August 15, 1138 B.C.E. The duration of Saros series 10 was 1316.2 years, and it contained 74 lunar eclipses.

## In technology

• Driving a racing car at ten-tenths is driving as fast as possible, on the limit.
• 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.
• Ten is the ASCII and Unicode code point for line feed.

## In religion

### Judaism

• The Ten Commandments that God gave to Moses (Exodus 20:3-17 and Deuteronomy 5:7-21) are considered a cornerstone of Judaism and Christianity.[6]
• In Deuteronomy 26:12, the Torah commands Jews to give one-tenth of their produce to the poor (Maaser Ani). From this verse and an earlier verse (Deut. 14:22), there derives a practice for Jews to give one-tenth of all earnings to the poor.[7]
• Ten Plagues were inflicted on Egypt (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.

### Christianity

• People traditionally gave one-tenth of their produce as tithe. 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 music

• The interval of a major or minor tenth is an octave plus a major or minor third.

## In sports

• In rugby union, the fly-half wears the 10 shirt.
• In blackjack, the Ten, Jack, Queen and King are all worth 10 points.
• In ten-pin bowling, 10 pins are arranged in a triangular pattern and there are 10 frames per game.
• In football (soccer), 10 is the jersey number of many of the best players, particularly attacking midfielders, especially players from South America. 'Number 10' player is most often used as a synonym for the team's playmaker.
• Ten is the highest score possible in Olympics competitions.
• 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 baseball, there are always at least 10 players on the field at a time (including the batter).

## Miscellany

10 playing cards of all four suits.
• Increasing a quantity by one order of magnitude means increasing it 10-fold. Conversely, decreasing it by an order of magnitude means decreasing it 10-fold.
• The term decimate literally means to reduce something by one-tenth, although it is also means reducing something drastically.
• A group of ten items or a ten-year time period is called a decade.
• A decapod crustacean has ten limbs.
• 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.
• Someone who scores perfectly is said to have scored "a perfect ten."
• Counting from one to ten before speaking is often done in order to cool one's temper.
• In Chinese astrology, the 10 Heavenly Stems refer to a cyclic number system that is used also for time reckoning.
• The ordinal adjective for ten is denary.
• A 1977 short documentary film Powers of Ten depicts the relative scale of the Universe in factors of ten (orders of magnitude).
• Ten is the number of dots in a tetractys.

## Notes

1. A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.
2. A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.
3. A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.
4. Solar Eclipses of Saros 0 to 180 NASA Eclipse Web Site. Retrieved August 20, 2008.
5. Lunar Eclipses of Saros Series 1 to 175 NASA Eclipse Web Site. Retrieved August 20, 2008.
6. Harold Lindsell (ed.), Harper Study Bible: The Holy Bible Revised Standard Version (Grand Rapids, MI: Zondervan Bible Publishers, 1971).
7. Parshas VaYeitzei: Ma'aser Kesafim Retrieved August 22, 2008.

## References

• Flegg, Graham. 2002. Numbers: Their History and Meaning. Mineola, NY: Dover Publications. ISBN 0486421651
• Higgins, Peter M. 2008. Number Story: From Counting to Cryptography. London: Copernicus. ISBN 978-1848000001
• Ifrah, Georges. 2000. The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos et al. New York: Wiley. ISBN 0471393401
• McLeish, John. 1994. The Story of Numbers: How Mathematics Has Shaped Civilization. New York: Fawcett Columbine. ISBN 0449909387
• Menninger, Karl. 1992. Number Words and Number Symbols: A Cultural History of Numbers. New York: Dover Publications. ISBN 0486270963
• Wells, D. G. 1998. The Penguin Dictionary of Curious and Interesting Numbers. Rev. ed. London, UK: Penguin Books. ISBN 0140261494