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The decimal numeral system is the most usual way of writing numbers. It has ten as a starting point, or base. It is sometimes called the base ten or denary numeral system. The word "decimal" is also used instead of the word "period" to mean the dot (".") that is sometimes used to separate the positions of the numbers in this system. Indeed, the dot is the default decimal separator in English-speaking countries.[1][2]

Decimal notation

Decimal notation is the writing of numbers in the base-ten numeral system, which uses various symbols (called digits) for no more than ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9[3]) to represent any numbers, no matter how large. These digits are often used with a decimal separator(such as "." or ","),[1][2] which indicates the start of a fractional part, and with one of the sign symbols + (positive) or − (negative) in front of the numerals to indicate sign.

There are only two truly positional decimal systems in ancient civilization: the Chinese counting rods system and Hindu-Arabic numeral system. Both required no more than ten symbols, while other numeral systems, such as Babylonian base-60 system, require more symbols.

Other rational numbers

Any rational number can be expressed as a unique decimal expansion. It may have to end with recurring decimals.

Ten is the product of the first and third prime numbers, is one greater than the square of the second prime number, and is one less than the fifth prime number. This leads to plenty of simple decimal fractions:

1/2 = 0.5
1/3 = 0.333333 ... (with 3 repeating forever, also called recurring)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.166666 ... (with 6 recurring)
1/7 = 0.142857 ... (with 142857 recurring)
1/8 = 0.125
1/9 = 0.111111 ... (with 1 recurring)
1/10 = 0.1
1/11 = 0.090909 ... (with 09 recurring)
1/12 = 0.083333 ... (with 3 recurring)
1/81 = 0.012345679012 ... (with 012345679 recurring)


Timeline of decimal usage

Natural languages

A straightforward decimal system, in which 11 is expressed as ten-one and 23 as two-ten-three, is found in Chinese languages except Wu, and in Vietnamese with a few irregularities. Japanese, Korean, and Thai have imported the Chinese decimal system. Many other languages with a decimal system have special words for teens and decades.

Incan languages such as Quechua and Aymara have an almost straightforward decimal system, in which 11 is expressed as ten with one and 23 as two-ten with three.

Some psychologists suggest irregularities of numerals in a language may hinder children's counting ability (Azar 1999).

Related pages


  1. 1.0 1.1 "Compendium of Mathematical Symbols" (in en-US). 2020-03-01. 
  2. 2.0 2.1 Weisstein, Eric W.. "Decimal Point" (in en). 
  3. Weisstein, Eric W.. "Decimal" (in en). 


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