# decimal

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## decimal

**1.**a fraction that has a denominator of a power of ten, the power depending on or deciding the decimal place. It is indicated by a decimal point to the left of the numerator, the denominator being omitted. Zeros are inserted between the point and the numerator, if necessary, to obtain the correct decimal place

**2.**any number used in the decimal system

**3.**

**a.**relating to or using powers of ten

**b.**of the base ten

**4.**expressed as a decimal

## Decimal

a fraction whose denominator is a whole power of the number 10. The decimal is written without a denominator, setting off in the numerator to the right of the decimal point as many digits as there are zeros in the denominator (for example, 485,634/1,000 = 485.634 and 3/100 = 0.03). In such notation, the part to the left of the decimal point designates the integer part of the fraction. The first digit after the decimal point designates the number of tenths; the second, the number of hundredths; and so forth.

The decimal notation of rational numbers whose denominator does not have other prime factors except 2 and 5 contains a finite number of digits (for example, 4/25 = 0.16). In general, the digits in the decimal notation of a rational number begin repeating at some position; such a number is an infinite repeating decimal (for example, 7/6 = 1.1666 …). Irrational numbers are nonrepeating infinite decimals (for example, = 1.41421 . … In all cases, the decimal of *a _{k}*

*a*…

_{k-1}*a*

_{0}*b*

_{1}*b*… can be written in the form

_{2}where *a*_{k}, *a _{k-1}*, … ,

*a*

_{0},

*b*

_{1}

*b*

_{2}, are the numerals 0, 1, 2, … , 9 (

*a*

_{k}≠ 0) in the corresponding digit of the number. For example, 382.1274 = 3 x 10

^{2}+ 8 × 10 + 2 + 1/10 + 2/10

^{2}+ 7/10

^{3}+ 4/10

^{4}, that is, here

*a*= 3,

_{2}*a*

_{1}= 8,

*a*= 2,

_{0}*b*

_{1}= 1,

*b*

_{2}= 2,

*b*

_{3}= 7, and

*b*

_{4}= 4. Decimals were already used in the 14th-15th centuries. The Samarkand mathematician Al Kashi described the decimal system in 1427. In Europe, the decimal was introduced by S. Stevin in 1584.