# 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 akak-1a0b1b2 … can be written in the form

where ak, ak-1, … , a0, b1b2, are the numerals 0, 1, 2, … , 9 (ak ≠ 0) in the corresponding digit of the number. For example, 382.1274 = 3 x 102 + 8 × 10 + 2 + 1/10 + 2/102 + 7/103 + 4/104, that is, here a2 = 3, a1 = 8,a0 = 2, b1 = 1, b2 = 2, b3 = 7, and b4 = 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.

## decimal

[′des·məl]
(mathematics)
A number expressed in the scale of tens.

## decimal

Meaning 10. The numbering system used by humans, which is based on 10 digits. In contrast, computers use binary numbers because it is easier to design electronic systems that can maintain two states rather than 10.
References in periodicals archive ?
FC 9 (P, K): A Feistel-cycle cipher encrypting all nine digit decimal values using key K.
H (P): A hash function from four digit decimal values to an arbitrary bit string.
In addition, sequential samples from several patients were included in the study (represented by the decimal values in Table 1) and the data from these samples show trends similar to those observed in the composite with single samples.
However, if you asked when the United Kingdom and the United States are going to introduce the process of changing their current measures of length and capacity, square and cubic measures, into decimal values, things are not so obvious.
By using the playdough materials, students are able to create the decimal values using concrete materials to match the written notation on the cards.
Once the concept of decimal values and notation is formed through these concrete experiences, students appear to have very little difficulty moving to abstract notation and processes.
Experiences with many children in the middle grades indicate that they have poor decimal concepts and lack fundamental skills in working with decimal values.
Third, they learn how decimal values grow and how their numerical representations change as tenths or hundredths are added repeatedly.
In this activity, students are enticed to connect a variety of ideas about decimal fractions, including various verbal and symbolic representations; relationships among wholes, tenths, and hundredths; and comparisons of decimal values.

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